subodh

Document Sample
subodh Powered By Docstoc
					                                               Features of string
                                              scale physics in the
                                                     CMB

                                               Subodh P. Patil

                                              Introductory
                                              remarks
                                              Priors and
                                              degeneracies
Features of string scale physics in the CMB   Biases in our priors?
                                              Outline

                                              When UV physics
                                              does not decouple
                                              Our highest energy
                Subodh P. Patil               probe?
                                              Probing
                                              compactifications?

            CPhT, Ecole Polytechnique &       Inflation with a
                                              mass hierarchy
                                    e
          LPTENS, Ecole Normale Sup´rieure    Bends in field space
                                              Features in the power
                                              spectrum

     CEFIPRA workshop, ENS, May 13th 2011
                                                                Features of string
What is the CMB telling us?                                    scale physics in the
                                                                      CMB
Big bang cosmology predicts a relic background of photons       Subodh P. Patil
with a perfect blackbody spectrum.
                                                               Introductory
     It’s overall isotropy (+ homogeneity) confirms the large   remarks
                                                               Priors and
     scale homogeneity + isotropy of our Hubble patch.         degeneracies
                                                               Biases in our priors?
                                                               Outline

                                                               When UV physics
                                                               does not decouple
                                                               Our highest energy
                                                               probe?
                                                               Probing
                                                               compactifications?

                                                               Inflation with a
                                                               mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
What is the CMB telling us?                                    scale physics in the
                                                                      CMB
Big bang cosmology predicts a relic background of photons       Subodh P. Patil
with a perfect blackbody spectrum.
                                                               Introductory
     It’s overall isotropy (+ homogeneity) confirms the large   remarks
                                                               Priors and
     scale homogeneity + isotropy of our Hubble patch.         degeneracies
                                                               Biases in our priors?
     It’s anisotropies (δT /T ∼ 10−5 ) provides a              Outline

                                                               When UV physics
     topographical map of gravitational potential at last      does not decouple
     scattering T ∼ 13.6eV .                                   Our highest energy
                                                               probe?
                                                               Probing
                                                               compactifications?

                                                               Inflation with a
                                                               mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
What is the CMB telling us?                                    scale physics in the
                                                                      CMB
Big bang cosmology predicts a relic background of photons       Subodh P. Patil
with a perfect blackbody spectrum.
                                                               Introductory
     It’s overall isotropy (+ homogeneity) confirms the large   remarks
                                                               Priors and
     scale homogeneity + isotropy of our Hubble patch.         degeneracies
                                                               Biases in our priors?
     It’s anisotropies (δT /T ∼ 10−5 ) provides a              Outline

                                                               When UV physics
     topographical map of gravitational potential at last      does not decouple
     scattering T ∼ 13.6eV .                                   Our highest energy
                                                               probe?
                                                               Probing
     ds 2 = (1 − 2φ)dt 2 + (1 + 2φ)a2 (t)dx i dx i             compactifications?

                                                               Inflation with a
                                                               mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
What is the CMB telling us?                                    scale physics in the
                                                                      CMB
Big bang cosmology predicts a relic background of photons       Subodh P. Patil
with a perfect blackbody spectrum.
                                                               Introductory
     It’s overall isotropy (+ homogeneity) confirms the large   remarks
                                                               Priors and
     scale homogeneity + isotropy of our Hubble patch.         degeneracies
                                                               Biases in our priors?
     It’s anisotropies (δT /T ∼ 10−5 ) provides a              Outline

                                                               When UV physics
     topographical map of gravitational potential at last      does not decouple
     scattering T ∼ 13.6eV .                                   Our highest energy
                                                               probe?
                                                               Probing
     ds 2 = (1 − 2φ)dt 2 + (1 + 2φ)a2 (t)dx i dx i             compactifications?

                                                               Inflation with a
     δT /T = vE − φ + δT /Trad                                 mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
What is the CMB telling us?                                    scale physics in the
                                                                      CMB
Big bang cosmology predicts a relic background of photons       Subodh P. Patil
with a perfect blackbody spectrum.
                                                               Introductory
     It’s overall isotropy (+ homogeneity) confirms the large   remarks
                                                               Priors and
     scale homogeneity + isotropy of our Hubble patch.         degeneracies
                                                               Biases in our priors?
     It’s anisotropies (δT /T ∼ 10−5 ) provides a              Outline

                                                               When UV physics
     topographical map of gravitational potential at last      does not decouple
     scattering T ∼ 13.6eV .                                   Our highest energy
                                                               probe?
                                                               Probing
     ds 2 = (1 − 2φ)dt 2 + (1 + 2φ)a2 (t)dx i dx i             compactifications?

                                                               Inflation with a
     δT /T = vE − φ + δT /Trad                                 mass hierarchy
                                                               Bends in field space
     δT /T (k) = Ω(k)Pφ (k)                                    Features in the power
                                                               spectrum
                                                                   Features of string
What is the CMB telling us?                                       scale physics in the
                                                                         CMB
Big bang cosmology predicts a relic background of photons          Subodh P. Patil
with a perfect blackbody spectrum.
                                                                  Introductory
     It’s overall isotropy (+ homogeneity) confirms the large      remarks
                                                                  Priors and
     scale homogeneity + isotropy of our Hubble patch.            degeneracies
                                                                  Biases in our priors?
     It’s anisotropies (δT /T ∼ 10−5 ) provides a                 Outline

                                                                  When UV physics
     topographical map of gravitational potential at last         does not decouple
     scattering T ∼ 13.6eV .                                      Our highest energy
                                                                  probe?
                                                                  Probing
     ds 2 = (1 − 2φ)dt 2 + (1 + 2φ)a2 (t)dx i dx i                compactifications?

                                                                  Inflation with a
     δT /T = vE − φ + δT /Trad                                    mass hierarchy
                                                                  Bends in field space
     δT /T (k) = Ω(k)Pφ (k)                                       Features in the power
                                                                  spectrum
     Ω(k) is the so-called transfer function ≈ 1 at the largest
     scales.
                                                                   Features of string
What is the CMB telling us?                                       scale physics in the
                                                                         CMB
Big bang cosmology predicts a relic background of photons          Subodh P. Patil
with a perfect blackbody spectrum.
                                                                  Introductory
     It’s overall isotropy (+ homogeneity) confirms the large      remarks
                                                                  Priors and
     scale homogeneity + isotropy of our Hubble patch.            degeneracies
                                                                  Biases in our priors?
     It’s anisotropies (δT /T ∼ 10−5 ) provides a                 Outline

                                                                  When UV physics
     topographical map of gravitational potential at last         does not decouple
     scattering T ∼ 13.6eV .                                      Our highest energy
                                                                  probe?
                                                                  Probing
     ds 2 = (1 − 2φ)dt 2 + (1 + 2φ)a2 (t)dx i dx i                compactifications?

                                                                  Inflation with a
     δT /T = vE − φ + δT /Trad                                    mass hierarchy
                                                                  Bends in field space
     δT /T (k) = Ω(k)Pφ (k)                                       Features in the power
                                                                  spectrum
     Ω(k) is the so-called transfer function ≈ 1 at the largest
     scales.
     Pφ (k) = k 3 |φ(k)|2 ∼ k ns −1 , with the so-called
     spectral index ns ≈ 1 in simple toy models of inflation.
                                                                   Features of string
What is the CMB telling us?                                       scale physics in the
                                                                         CMB
Big bang cosmology predicts a relic background of photons          Subodh P. Patil
with a perfect blackbody spectrum.
                                                                  Introductory
     It’s overall isotropy (+ homogeneity) confirms the large      remarks
                                                                  Priors and
     scale homogeneity + isotropy of our Hubble patch.            degeneracies
                                                                  Biases in our priors?
     It’s anisotropies (δT /T ∼ 10−5 ) provides a                 Outline

                                                                  When UV physics
     topographical map of gravitational potential at last         does not decouple
     scattering T ∼ 13.6eV .                                      Our highest energy
                                                                  probe?
                                                                  Probing
     ds 2 = (1 − 2φ)dt 2 + (1 + 2φ)a2 (t)dx i dx i                compactifications?

                                                                  Inflation with a
     δT /T = vE − φ + δT /Trad                                    mass hierarchy
                                                                  Bends in field space
     δT /T (k) = Ω(k)Pφ (k)                                       Features in the power
                                                                  spectrum
     Ω(k) is the so-called transfer function ≈ 1 at the largest
     scales.
     Pφ (k) = k 3 |φ(k)|2 ∼ k ns −1 , with the so-called
     spectral index ns ≈ 1 in simple toy models of inflation.
     We fit a combination of input seed spectrum + physics
     since last scattering to the data, allowing us to infer
     cosmological parameters.
                                Features of string
The cosmic ultrasound          scale physics in the
                                      CMB

                                Subodh P. Patil
Courtesy WMAP collaboration:
                               Introductory
                               remarks
                               Priors and
                               degeneracies
                               Biases in our priors?
                               Outline

                               When UV physics
                               does not decouple
                               Our highest energy
                               probe?
                               Probing
                               compactifications?

                               Inflation with a
                               mass hierarchy
                               Bends in field space
                               Features in the power
                               spectrum
                                                                Features of string
What exactly is the CMB telling us?                            scale physics in the
                                                                      CMB
Although the simplest models of single field inflation remain     Subodh P. Patil
compatible with current CMB experiments, a direct
                                                               Introductory
reconstruction of the primordial power spectrum is still       remarks
                                                               Priors and
limited by degeneracies in our priors and our systematics:     degeneracies
                                                               Biases in our priors?
     The actual raw data from WMAP has been extensively        Outline

     processed– binning in l-space, ‘outliers’ accorded less   When UV physics
                                                               does not decouple
     significance etc.                                          Our highest energy
                                                               probe?
                                                               Probing
                                                               compactifications?

                                                               Inflation with a
                                                               mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
What exactly is the CMB telling us?                            scale physics in the
                                                                      CMB
Although the simplest models of single field inflation remain     Subodh P. Patil
compatible with current CMB experiments, a direct
                                                               Introductory
reconstruction of the primordial power spectrum is still       remarks
                                                               Priors and
limited by degeneracies in our priors and our systematics:     degeneracies
                                                               Biases in our priors?
     The actual raw data from WMAP has been extensively        Outline

     processed– binning in l-space, ‘outliers’ accorded less   When UV physics
                                                               does not decouple
     significance etc.                                          Our highest energy
                                                               probe?
                                                               Probing
     The actual data, unbinned (courtesy NASA):                compactifications?

                                                               Inflation with a
                                                               mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                               Features of string
Theory dependent observations?                                scale physics in the
                                                                     CMB
Although an almost scale invariant spectrum ‘predicts’ what    Subodh P. Patil
is ‘observed’ in the CMB, could it be that some very
                                                              Introductory
interesting physics has been glossed over in this approach?   remarks
                                                              Priors and
      In particular, could a non-scale invariant spectrum     degeneracies
                                                              Biases in our priors?
      better fit the data?                                     Outline

                                                              When UV physics
                                                              does not decouple
                                                              Our highest energy
                                                              probe?
                                                              Probing
                                                              compactifications?

                                                              Inflation with a
                                                              mass hierarchy
                                                              Bends in field space
                                                              Features in the power
                                                              spectrum
                                                                   Features of string
Theory dependent observations?                                    scale physics in the
                                                                         CMB
Although an almost scale invariant spectrum ‘predicts’ what        Subodh P. Patil
is ‘observed’ in the CMB, could it be that some very
                                                                  Introductory
interesting physics has been glossed over in this approach?       remarks
                                                                  Priors and
      In particular, could a non-scale invariant spectrum         degeneracies
                                                                  Biases in our priors?
      better fit the data?                                         Outline

      Is a scale invariant spectrum even generic in a realistic   When UV physics
                                                                  does not decouple
      model of inflation?                                          Our highest energy
                                                                  probe?
                                                                  Probing
                                                                  compactifications?

                                                                  Inflation with a
                                                                  mass hierarchy
                                                                  Bends in field space
                                                                  Features in the power
                                                                  spectrum
                                                                   Features of string
Theory dependent observations?                                    scale physics in the
                                                                         CMB
Although an almost scale invariant spectrum ‘predicts’ what        Subodh P. Patil
is ‘observed’ in the CMB, could it be that some very
                                                                  Introductory
interesting physics has been glossed over in this approach?       remarks
                                                                  Priors and
      In particular, could a non-scale invariant spectrum         degeneracies
                                                                  Biases in our priors?
      better fit the data?                                         Outline

      Is a scale invariant spectrum even generic in a realistic   When UV physics
                                                                  does not decouple
      model of inflation?                                          Our highest energy
                                                                  probe?

      Be wary of data black box– hidden assumptions of            Probing
                                                                  compactifications?

      theorists creep in to the analysis. Hunt and Sarkar         Inflation with a
                                                                  mass hierarchy
      (arXiv:0706.2443): WMAP data can be better fit with          Bends in field space
                                                                  Features in the power
      a ‘bump’ in the spectrum with h = 0.44 and                  spectrum

      ΩM = 1 (better χ2 arises from the data ‘glitches’).
                                                                   Features of string
Theory dependent observations?                                    scale physics in the
                                                                         CMB
Although an almost scale invariant spectrum ‘predicts’ what        Subodh P. Patil
is ‘observed’ in the CMB, could it be that some very
                                                                  Introductory
interesting physics has been glossed over in this approach?       remarks
                                                                  Priors and
      In particular, could a non-scale invariant spectrum         degeneracies
                                                                  Biases in our priors?
      better fit the data?                                         Outline

      Is a scale invariant spectrum even generic in a realistic   When UV physics
                                                                  does not decouple
      model of inflation?                                          Our highest energy
                                                                  probe?

      Be wary of data black box– hidden assumptions of            Probing
                                                                  compactifications?

      theorists creep in to the analysis. Hunt and Sarkar         Inflation with a
                                                                  mass hierarchy
      (arXiv:0706.2443): WMAP data can be better fit with          Bends in field space
                                                                  Features in the power
      a ‘bump’ in the spectrum with h = 0.44 and                  spectrum

      ΩM = 1 (better χ2 arises from the data ‘glitches’).
      The quality of data available to us is due to vastly
      improve in the coming years (PLANCK, CMBPol)– we
      may be able to more accurately constrain (or even
      detect!) non-trivial non-gaussianities in the CMB (and
      thus test models containing comsic strings, stringy
      inflation, alternatives to inflation).
                                                                Features of string
Overview                                                       scale physics in the
                                                                      CMB
In addition to the importance of understanding what the         Subodh P. Patil
CMB is actually telling us about the primordial power
                                                               Introductory
spectrum, we also need to explore what features realistic      remarks
                                                               Priors and
models of inflation might actually be generating.               degeneracies
                                                               Biases in our priors?
     In the moments of the CMB, there is in principle a lot    Outline

                                                               When UV physics
     of information about the Lagrangian of inflation. The      does not decouple
     simplest analyses of the currently available data seems   Our highest energy
                                                               probe?
                                                               Probing
     to suggest:                                               compactifications?

                                                               Inflation with a
                                                               mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
Overview                                                       scale physics in the
                                                                      CMB
In addition to the importance of understanding what the         Subodh P. Patil
CMB is actually telling us about the primordial power
                                                               Introductory
spectrum, we also need to explore what features realistic      remarks
                                                               Priors and
models of inflation might actually be generating.               degeneracies
                                                               Biases in our priors?
     In the moments of the CMB, there is in principle a lot    Outline

                                                               When UV physics
     of information about the Lagrangian of inflation. The      does not decouple
     simplest analyses of the currently available data seems   Our highest energy
                                                               probe?
                                                               Probing
     to suggest:                                               compactifications?

                                                               Inflation with a
     One effective light degree of freedom at a fixed energy     mass hierarchy
     scale (long wavelength perturbations are adiabatic)       Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
Overview                                                       scale physics in the
                                                                      CMB
In addition to the importance of understanding what the         Subodh P. Patil
CMB is actually telling us about the primordial power
                                                               Introductory
spectrum, we also need to explore what features realistic      remarks
                                                               Priors and
models of inflation might actually be generating.               degeneracies
                                                               Biases in our priors?
     In the moments of the CMB, there is in principle a lot    Outline

                                                               When UV physics
     of information about the Lagrangian of inflation. The      does not decouple
     simplest analyses of the currently available data seems   Our highest energy
                                                               probe?
                                                               Probing
     to suggest:                                               compactifications?

                                                               Inflation with a
     One effective light degree of freedom at a fixed energy     mass hierarchy
     scale (long wavelength perturbations are adiabatic)       Bends in field space
                                                               Features in the power
                                                               spectrum
     Whose interactions with other fields appear to be
     constrained to be irrelevant (i.e. heavy physics is
     decoupled)
                                                                Features of string
Overview                                                       scale physics in the
                                                                      CMB
In addition to the importance of understanding what the         Subodh P. Patil
CMB is actually telling us about the primordial power
                                                               Introductory
spectrum, we also need to explore what features realistic      remarks
                                                               Priors and
models of inflation might actually be generating.               degeneracies
                                                               Biases in our priors?
     In the moments of the CMB, there is in principle a lot    Outline

                                                               When UV physics
     of information about the Lagrangian of inflation. The      does not decouple
     simplest analyses of the currently available data seems   Our highest energy
                                                               probe?
                                                               Probing
     to suggest:                                               compactifications?

                                                               Inflation with a
     One effective light degree of freedom at a fixed energy     mass hierarchy
     scale (long wavelength perturbations are adiabatic)       Bends in field space
                                                               Features in the power
                                                               spectrum
     Whose interactions with other fields appear to be
     constrained to be irrelevant (i.e. heavy physics is
     decoupled)
     With negligible self interactions (consistent with
     Gaussian statistics)
                                                                Features of string
Overview                                                       scale physics in the
                                                                      CMB
In addition to the importance of understanding what the         Subodh P. Patil
CMB is actually telling us about the primordial power
                                                               Introductory
spectrum, we also need to explore what features realistic      remarks
                                                               Priors and
models of inflation might actually be generating.               degeneracies
                                                               Biases in our priors?
     In the moments of the CMB, there is in principle a lot    Outline

                                                               When UV physics
     of information about the Lagrangian of inflation. The      does not decouple
     simplest analyses of the currently available data seems   Our highest energy
                                                               probe?
                                                               Probing
     to suggest:                                               compactifications?

                                                               Inflation with a
     One effective light degree of freedom at a fixed energy     mass hierarchy
     scale (long wavelength perturbations are adiabatic)       Bends in field space
                                                               Features in the power
                                                               spectrum
     Whose interactions with other fields appear to be
     constrained to be irrelevant (i.e. heavy physics is
     decoupled)
     With negligible self interactions (consistent with
     Gaussian statistics)
     Whose fluctuations were initially in the Bunch-Davies
     vacuum state.
                                                                   Features of string
Outline                                                           scale physics in the
                                                                         CMB
In this talk, we wish to discuss inflation in the setting where     Subodh P. Patil
it is an effective light direction in a multi-dimensional field
                                                                  Introductory
space (representative of inflation realized in string theory),     remarks
                                                                  Priors and
where we see that:                                                degeneracies
                                                                  Biases in our priors?
      Heavy physics does not necessarily decouple, and in         Outline

                                                                  When UV physics
      certain generic situations, can imprint itself on the CMB   does not decouple
      as superimposed damped oscillatory features (or,            Our highest energy
                                                                  probe?
                                                                  Probing
      truncating is not the same as integrating out).             compactifications?

                                                                  Inflation with a
                                                                  mass hierarchy
                                                                  Bends in field space
                                                                  Features in the power
                                                                  spectrum
                                                                   Features of string
Outline                                                           scale physics in the
                                                                         CMB
In this talk, we wish to discuss inflation in the setting where     Subodh P. Patil
it is an effective light direction in a multi-dimensional field
                                                                  Introductory
space (representative of inflation realized in string theory),     remarks
                                                                  Priors and
where we see that:                                                degeneracies
                                                                  Biases in our priors?
      Heavy physics does not necessarily decouple, and in         Outline

                                                                  When UV physics
      certain generic situations, can imprint itself on the CMB   does not decouple
      as superimposed damped oscillatory features (or,            Our highest energy
                                                                  probe?
                                                                  Probing
      truncating is not the same as integrating out).             compactifications?

                                                                  Inflation with a
      An effective theory for the perturbations can be written     mass hierarchy
      down with a modified speed of sound: correlated              Bends in field space
                                                                  Features in the power
                                                                  spectrum
      non-gaussian signatures.
                                                                   Features of string
Outline                                                           scale physics in the
                                                                         CMB
In this talk, we wish to discuss inflation in the setting where     Subodh P. Patil
it is an effective light direction in a multi-dimensional field
                                                                  Introductory
space (representative of inflation realized in string theory),     remarks
                                                                  Priors and
where we see that:                                                degeneracies
                                                                  Biases in our priors?
      Heavy physics does not necessarily decouple, and in         Outline

                                                                  When UV physics
      certain generic situations, can imprint itself on the CMB   does not decouple
      as superimposed damped oscillatory features (or,            Our highest energy
                                                                  probe?
                                                                  Probing
      truncating is not the same as integrating out).             compactifications?

                                                                  Inflation with a
      An effective theory for the perturbations can be written     mass hierarchy
      down with a modified speed of sound: correlated              Bends in field space
                                                                  Features in the power
                                                                  spectrum
      non-gaussian signatures.
      If representative of inflation in string theory, gives us
      information of the local geometry of field space:
      information about the particular string compactification.
                                                                   Features of string
Outline                                                           scale physics in the
                                                                         CMB
In this talk, we wish to discuss inflation in the setting where     Subodh P. Patil
it is an effective light direction in a multi-dimensional field
                                                                  Introductory
space (representative of inflation realized in string theory),     remarks
                                                                  Priors and
where we see that:                                                degeneracies
                                                                  Biases in our priors?
      Heavy physics does not necessarily decouple, and in         Outline

                                                                  When UV physics
      certain generic situations, can imprint itself on the CMB   does not decouple
      as superimposed damped oscillatory features (or,            Our highest energy
                                                                  probe?
                                                                  Probing
      truncating is not the same as integrating out).             compactifications?

                                                                  Inflation with a
      An effective theory for the perturbations can be written     mass hierarchy
      down with a modified speed of sound: correlated              Bends in field space
                                                                  Features in the power
                                                                  spectrum
      non-gaussian signatures.
      If representative of inflation in string theory, gives us
      information of the local geometry of field space:
      information about the particular string compactification.
      More generally, non-trivial information about some of
      the higher dimensional operators in the low effective
      field theory– information of the parent theory.
                                                               Features of string
The collaboration                                             scale physics in the
                                                                     CMB

                                                               Subodh P. Patil

                                                              Introductory
                                                              remarks
                                                              Priors and
                                                              degeneracies
                                                              Biases in our priors?
                                                              Outline
This work has been in done in a long standing collaboration   When UV physics
             u
with Ana Ach´carro, Jinn-Ouk Gong, Sjoerd Hardeman and        does not decouple
                                                              Our highest energy
Gonzalo A. Palma                                              probe?
                                                              Probing
                                                              compactifications?
    arXiv:1005.3848                                           Inflation with a
                                                              mass hierarchy
    arXiv:1010.3693                                           Bends in field space
                                                              Features in the power
    arXiv:11xx.xxxx                                           spectrum
                                                                Features of string
Inflation– an empirical probe of the highest                    scale physics in the
                                                                      CMB
energies?                                                       Subodh P. Patil

Inflation is the putative quasi exponential expansion of        Introductory
                                                               remarks
spacetime at some early epoch which sets up the initial        Priors and
                                                               degeneracies
conditions for the hot big bang– homogeneous∗ , isotropic∗ ,   Biases in our priors?
                                                               Outline
flat, thermalized initial conditions absent of dangerous        When UV physics
topological relics.                                            does not decouple
                                                               Our highest energy
                                                               probe?
    Obtained by positing some effective scalar field, whose      Probing
                                                               compactifications?
    energy momentum tensor                                     Inflation with a
      µ
    Tν = diag [−ρ, p, p, p] satisfies ρ ≈ −p .                  mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
Inflation– an empirical probe of the highest                    scale physics in the
                                                                      CMB
energies?                                                       Subodh P. Patil

Inflation is the putative quasi exponential expansion of        Introductory
                                                               remarks
spacetime at some early epoch which sets up the initial        Priors and
                                                               degeneracies
conditions for the hot big bang– homogeneous∗ , isotropic∗ ,   Biases in our priors?
                                                               Outline
flat, thermalized initial conditions absent of dangerous        When UV physics
topological relics.                                            does not decouple
                                                               Our highest energy
                                                               probe?
    Obtained by positing some effective scalar field, whose      Probing
                                                               compactifications?
    energy momentum tensor                                     Inflation with a
      µ
    Tν = diag [−ρ, p, p, p] satisfies ρ ≈ −p .                  mass hierarchy
                                                               Bends in field space
                                                               Features in the power
    In an FRW slicing, results in the expansion                spectrum

                         2
    a(t) ∼ Exp[ V /3Mpl t]
                                                                Features of string
Inflation– an empirical probe of the highest                    scale physics in the
                                                                      CMB
energies?                                                       Subodh P. Patil

Inflation is the putative quasi exponential expansion of        Introductory
                                                               remarks
spacetime at some early epoch which sets up the initial        Priors and
                                                               degeneracies
conditions for the hot big bang– homogeneous∗ , isotropic∗ ,   Biases in our priors?
                                                               Outline
flat, thermalized initial conditions absent of dangerous        When UV physics
topological relics.                                            does not decouple
                                                               Our highest energy
                                                               probe?
    Obtained by positing some effective scalar field, whose      Probing
                                                               compactifications?
    energy momentum tensor                                     Inflation with a
      µ
    Tν = diag [−ρ, p, p, p] satisfies ρ ≈ −p .                  mass hierarchy
                                                               Bends in field space
                                                               Features in the power
    In an FRW slicing, results in the expansion                spectrum

                         2
    a(t) ∼ Exp[ V /3Mpl t]
    Traditionally: L = 1 ∂µ φ∂ν φ − V (φ)
                       2
                                                                Features of string
Inflation– an empirical probe of the highest                    scale physics in the
                                                                      CMB
energies?                                                       Subodh P. Patil

Inflation is the putative quasi exponential expansion of        Introductory
                                                               remarks
spacetime at some early epoch which sets up the initial        Priors and
                                                               degeneracies
conditions for the hot big bang– homogeneous∗ , isotropic∗ ,   Biases in our priors?
                                                               Outline
flat, thermalized initial conditions absent of dangerous        When UV physics
topological relics.                                            does not decouple
                                                               Our highest energy
                                                               probe?
    Obtained by positing some effective scalar field, whose      Probing
                                                               compactifications?
    energy momentum tensor                                     Inflation with a
      µ
    Tν = diag [−ρ, p, p, p] satisfies ρ ≈ −p .                  mass hierarchy
                                                               Bends in field space
                                                               Features in the power
    In an FRW slicing, results in the expansion                spectrum

                         2
    a(t) ∼ Exp[ V /3Mpl t]
    Traditionally: L = 1 ∂µ φ∂ν φ − V (φ)
                       2
    Inflation happens if we are at a point in field space such
          ˙
    that φ2                2
               V → := Mpl V 2 /3V 2       1
                                                                Features of string
Inflation– an empirical probe of the highest                    scale physics in the
                                                                      CMB
energies?                                                       Subodh P. Patil

Inflation is the putative quasi exponential expansion of        Introductory
                                                               remarks
spacetime at some early epoch which sets up the initial        Priors and
                                                               degeneracies
conditions for the hot big bang– homogeneous∗ , isotropic∗ ,   Biases in our priors?
                                                               Outline
flat, thermalized initial conditions absent of dangerous        When UV physics
topological relics.                                            does not decouple
                                                               Our highest energy
                                                               probe?
    Obtained by positing some effective scalar field, whose      Probing
                                                               compactifications?
    energy momentum tensor                                     Inflation with a
      µ
    Tν = diag [−ρ, p, p, p] satisfies ρ ≈ −p .                  mass hierarchy
                                                               Bends in field space
                                                               Features in the power
    In an FRW slicing, results in the expansion                spectrum

                         2
    a(t) ∼ Exp[ V /3Mpl t]
    Traditionally: L = 1 ∂µ φ∂ν φ − V (φ)
                       2
    Inflation happens if we are at a point in field space such
          ˙
    that φ2                2
               V → := Mpl V 2 /3V 2        1
    and φ¨       ˙           2
             3H φ → η := Mpl V /V        1
                                                                  Features of string
Inflation– an empirical probe of the highest                      scale physics in the
                                                                        CMB
energies?                                                         Subodh P. Patil

                                                                 Introductory
Provided the ‘slow roll’ conditions can be met, inflation lasts   remarks
                                                                 Priors and
for sufficiently long to give us a viable starting point for big   degeneracies
                                                                 Biases in our priors?
bang cosmology.                                                  Outline

                                                                 When UV physics
    It also provides us with the initial seed structure of       does not decouple
                                                                 Our highest energy
    gravitational perturbations– a scale invariant spectrum      probe?
                                                                 Probing
    of adiabatic co-moving curvature perturbations               compactifications?
                                        2
    PR (k) := k 3 |R(k)|2 = (2π)3 H2 k 3 |δφ(k)|2 ∼ k ns −1
                                      ˙
                                      φ
                                                                 Inflation with a
                                                                 mass hierarchy
                                      0                          Bends in field space
                                                                 Features in the power
                                                                 spectrum
                                                                  Features of string
Inflation– an empirical probe of the highest                      scale physics in the
                                                                        CMB
energies?                                                         Subodh P. Patil

                                                                 Introductory
Provided the ‘slow roll’ conditions can be met, inflation lasts   remarks
                                                                 Priors and
for sufficiently long to give us a viable starting point for big   degeneracies
                                                                 Biases in our priors?
bang cosmology.                                                  Outline

                                                                 When UV physics
    It also provides us with the initial seed structure of       does not decouple
                                                                 Our highest energy
    gravitational perturbations– a scale invariant spectrum      probe?
                                                                 Probing
    of adiabatic co-moving curvature perturbations               compactifications?
                                        2
    PR (k) := k 3 |R(k)|2 = (2π)3 H2 k 3 |δφ(k)|2 ∼ k ns −1
                                      ˙
                                      φ
                                                                 Inflation with a
                                                                 mass hierarchy
                                      0                          Bends in field space
    ... with the amplitude tunable such that                     Features in the power
                                                                 spectrum

    δT /T ∼ 10−5 :
                               2
    PR (k) ∼ H 4 /φ2 ∼ (2π)3 H (k) ≈ 2.5 × 10−9
                   ˙
                     0        M2pl
                                                                  Features of string
Inflation– an empirical probe of the highest                      scale physics in the
                                                                        CMB
energies?                                                         Subodh P. Patil

                                                                 Introductory
Provided the ‘slow roll’ conditions can be met, inflation lasts   remarks
                                                                 Priors and
for sufficiently long to give us a viable starting point for big   degeneracies
                                                                 Biases in our priors?
bang cosmology.                                                  Outline

                                                                 When UV physics
    It also provides us with the initial seed structure of       does not decouple
                                                                 Our highest energy
    gravitational perturbations– a scale invariant spectrum      probe?
                                                                 Probing
    of adiabatic co-moving curvature perturbations               compactifications?
                                        2
    PR (k) := k 3 |R(k)|2 = (2π)3 H2 k 3 |δφ(k)|2 ∼ k ns −1
                                      ˙
                                      φ
                                                                 Inflation with a
                                                                 mass hierarchy
                                      0                          Bends in field space
    ... with the amplitude tunable such that                     Features in the power
                                                                 spectrum

    δT /T ∼ 10−5 :
                               2
    PR (k) ∼ H 4 /φ2 ∼ (2π)3 H (k) ≈ 2.5 × 10−9
                   ˙
                     0        M2pl

    Which implies that the scale of inflation is set by:
    H    1/2 1015 GeV
                                                                  Features of string
Inflation– an empirical probe of the highest                      scale physics in the
                                                                        CMB
energies?                                                         Subodh P. Patil

                                                                 Introductory
Provided the ‘slow roll’ conditions can be met, inflation lasts   remarks
                                                                 Priors and
for sufficiently long to give us a viable starting point for big   degeneracies
                                                                 Biases in our priors?
bang cosmology.                                                  Outline

                                                                 When UV physics
    It also provides us with the initial seed structure of       does not decouple
                                                                 Our highest energy
    gravitational perturbations– a scale invariant spectrum      probe?
                                                                 Probing
    of adiabatic co-moving curvature perturbations               compactifications?
                                        2
    PR (k) := k 3 |R(k)|2 = (2π)3 H2 k 3 |δφ(k)|2 ∼ k ns −1
                                      ˙
                                      φ
                                                                 Inflation with a
                                                                 mass hierarchy
                                      0                          Bends in field space
    ... with the amplitude tunable such that                     Features in the power
                                                                 spectrum

    δT /T ∼ 10−5 :
                               2
    PR (k) ∼ H 4 /φ2 ∼ (2π)3 H (k) ≈ 2.5 × 10−9
                   ˙
                     0        M2pl

    Which implies that the scale of inflation is set by:
    H    1/2 1015 GeV

    This begs the question: what exactly is the inflaton?
                                                                Features of string
Non decoupling of heavy physics?                               scale physics in the
                                                                      CMB
It is the parameters of the effective inflaton action that we     Subodh P. Patil
require to satisfy the slow roll requirements. It seems that
                                                               Introductory
heavy physics can only manifest as irrelevant (Planck          remarks
                                                               Priors and
suppressed) operators.                                         degeneracies
                                                               Biases in our priors?
      However heavy physics does not always decouple so        Outline

      cleanly from low energy physics. There are certain       When UV physics
                                                               does not decouple
      situations in which the conditions underlying the        Our highest energy
                                                               probe?

      decoupling theorem (Appelquist, Carrazone) may not be    Probing
                                                               compactifications?

      met:                                                     Inflation with a
                                                               mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
Non decoupling of heavy physics?                               scale physics in the
                                                                      CMB
It is the parameters of the effective inflaton action that we     Subodh P. Patil
require to satisfy the slow roll requirements. It seems that
                                                               Introductory
heavy physics can only manifest as irrelevant (Planck          remarks
                                                               Priors and
suppressed) operators.                                         degeneracies
                                                               Biases in our priors?
      However heavy physics does not always decouple so        Outline

      cleanly from low energy physics. There are certain       When UV physics
                                                               does not decouple
      situations in which the conditions underlying the        Our highest energy
                                                               probe?

      decoupling theorem (Appelquist, Carrazone) may not be    Probing
                                                               compactifications?

      met:                                                     Inflation with a
                                                               mass hierarchy
      When the heavy sectors and the light sectors             Bends in field space
                                                               Features in the power
      dynamically mix as inflation progresses                   spectrum
                                                                Features of string
Non decoupling of heavy physics?                               scale physics in the
                                                                      CMB
It is the parameters of the effective inflaton action that we     Subodh P. Patil
require to satisfy the slow roll requirements. It seems that
                                                               Introductory
heavy physics can only manifest as irrelevant (Planck          remarks
                                                               Priors and
suppressed) operators.                                         degeneracies
                                                               Biases in our priors?
      However heavy physics does not always decouple so        Outline

      cleanly from low energy physics. There are certain       When UV physics
                                                               does not decouple
      situations in which the conditions underlying the        Our highest energy
                                                               probe?

      decoupling theorem (Appelquist, Carrazone) may not be    Probing
                                                               compactifications?

      met:                                                     Inflation with a
                                                               mass hierarchy
      When the heavy sectors and the light sectors             Bends in field space
                                                               Features in the power
      dynamically mix as inflation progresses                   spectrum

      When there is an induced time dependence in the heavy
      sector through the dynamics of inflation such that the
      adiabatic approximation is violated
                                                                Features of string
Non decoupling of heavy physics?                               scale physics in the
                                                                      CMB
It is the parameters of the effective inflaton action that we     Subodh P. Patil
require to satisfy the slow roll requirements. It seems that
                                                               Introductory
heavy physics can only manifest as irrelevant (Planck          remarks
                                                               Priors and
suppressed) operators.                                         degeneracies
                                                               Biases in our priors?
      However heavy physics does not always decouple so        Outline

      cleanly from low energy physics. There are certain       When UV physics
                                                               does not decouple
      situations in which the conditions underlying the        Our highest energy
                                                               probe?

      decoupling theorem (Appelquist, Carrazone) may not be    Probing
                                                               compactifications?

      met:                                                     Inflation with a
                                                               mass hierarchy
      When the heavy sectors and the light sectors             Bends in field space
                                                               Features in the power
      dynamically mix as inflation progresses                   spectrum

      When there is an induced time dependence in the heavy
      sector through the dynamics of inflation such that the
      adiabatic approximation is violated
      More exotically, when we are not dealing with local
      EFT’s that can mix up scales via loop effects e.g:
      UV/IR mode mixing induced by non-commutative
      effects in brane inflation (SP, G.A.Palma 0906.4727)
                                                                 Features of string
Non decoupling of heavy directions?                             scale physics in the
                                                                       CMB

                                                                 Subodh P. Patil
Consider a typical 4-d low energy effective action resulting
describing a particular string compactification, or the scalar   Introductory
                                                                remarks
sector of some supergravity theory:                             Priors and
                                                                degeneracies
            √           M2                                      Biases in our priors?
     S=       −g d 4 x 2Pl R − 1 γab g µν ∂µ φa ∂ν φb − V (φ)
                                 2
                                                                Outline

                                                                When UV physics
                                                                does not decouple
                                                                Our highest energy
                                                                probe?
                                                                Probing
                                                                compactifications?

                                                                Inflation with a
                                                                mass hierarchy
                                                                Bends in field space
                                                                Features in the power
                                                                spectrum
                                                                 Features of string
Non decoupling of heavy directions?                             scale physics in the
                                                                       CMB

                                                                 Subodh P. Patil
Consider a typical 4-d low energy effective action resulting
describing a particular string compactification, or the scalar   Introductory
                                                                remarks
sector of some supergravity theory:                             Priors and
                                                                degeneracies
            √           M2                                      Biases in our priors?
     S=       −g d 4 x 2Pl R − 1 γab g µν ∂µ φa ∂ν φb − V (φ)
                                 2
                                                                Outline

                                                                When UV physics
    The fields φa coordinatize some field manifold M with         does not decouple
                                                                Our highest energy
                     1
    connection Γa = 2 γ ad (∂b γdc + ∂c γbd − ∂d γbc )
                bc
                                                                probe?
                                                                Probing
                                                                compactifications?

                                                                Inflation with a
                                                                mass hierarchy
                                                                Bends in field space
                                                                Features in the power
                                                                spectrum
                                                                 Features of string
Non decoupling of heavy directions?                             scale physics in the
                                                                       CMB

                                                                 Subodh P. Patil
Consider a typical 4-d low energy effective action resulting
describing a particular string compactification, or the scalar   Introductory
                                                                remarks
sector of some supergravity theory:                             Priors and
                                                                degeneracies
            √           M2                                      Biases in our priors?
     S=       −g d 4 x 2Pl R − 1 γab g µν ∂µ φa ∂ν φb − V (φ)
                                 2
                                                                Outline

                                                                When UV physics
    The fields φa coordinatize some field manifold M with         does not decouple
                                                                Our highest energy
                     1
    connection Γa = 2 γ ad (∂b γdc + ∂c γbd − ∂d γbc )
                bc
                                                                probe?
                                                                Probing
                                                                compactifications?
    And the associated Riemann tensor:                          Inflation with a
    Ra bcd = ∂c Γa − ∂d Γa + Γa Γe − Γa Γe
                 bd      bc   ce db    de cb
                                                                mass hierarchy
                                                                Bends in field space
                                                                Features in the power
                                                                spectrum
                                                                 Features of string
Non decoupling of heavy directions?                             scale physics in the
                                                                       CMB

                                                                 Subodh P. Patil
Consider a typical 4-d low energy effective action resulting
describing a particular string compactification, or the scalar   Introductory
                                                                remarks
sector of some supergravity theory:                             Priors and
                                                                degeneracies
            √           M2                                      Biases in our priors?
     S=       −g d 4 x 2Pl R − 1 γab g µν ∂µ φa ∂ν φb − V (φ)
                                 2
                                                                Outline

                                                                When UV physics
    The fields φa coordinatize some field manifold M with         does not decouple
                                                                Our highest energy
                     1
    connection Γa = 2 γ ad (∂b γdc + ∂c γbd − ∂d γbc )
                bc
                                                                probe?
                                                                Probing
                                                                compactifications?
    And the associated Riemann tensor:                          Inflation with a
    Ra bcd = ∂c Γa − ∂d Γa + Γa Γe − Γa Γe
                 bd      bc   ce db    de cb
                                                                mass hierarchy
                                                                Bends in field space
                                                                Features in the power
    The equations of motion are given by                        spectrum

     φa + Γa g µν ∂µ φb ∂ν φc = ∂V /∂φa
           bc
                                                                 Features of string
Non decoupling of heavy directions?                             scale physics in the
                                                                       CMB

                                                                 Subodh P. Patil
Consider a typical 4-d low energy effective action resulting
describing a particular string compactification, or the scalar   Introductory
                                                                remarks
sector of some supergravity theory:                             Priors and
                                                                degeneracies
            √           M2                                      Biases in our priors?
     S=       −g d 4 x 2Pl R − 1 γab g µν ∂µ φa ∂ν φb − V (φ)
                                 2
                                                                Outline

                                                                When UV physics
    The fields φa coordinatize some field manifold M with         does not decouple
                                                                Our highest energy
                     1
    connection Γa = 2 γ ad (∂b γdc + ∂c γbd − ∂d γbc )
                bc
                                                                probe?
                                                                Probing
                                                                compactifications?
    And the associated Riemann tensor:                          Inflation with a
    Ra bcd = ∂c Γa − ∂d Γa + Γa Γe − Γa Γe
                 bd      bc   ce db    de cb
                                                                mass hierarchy
                                                                Bends in field space
                                                                Features in the power
    The equations of motion are given by                        spectrum

     φa + Γa g µν ∂µ φb ∂ν φc = ∂V /∂φa
           bc
    We note that we can associate an energy scale
    associated with the curvature of M : R ∼ Λ−2 .
                                               M
                                                                 Features of string
Non decoupling of heavy directions?                             scale physics in the
                                                                       CMB

                                                                 Subodh P. Patil
Consider a typical 4-d low energy effective action resulting
describing a particular string compactification, or the scalar   Introductory
                                                                remarks
sector of some supergravity theory:                             Priors and
                                                                degeneracies
            √           M2                                      Biases in our priors?
     S=       −g d 4 x 2Pl R − 1 γab g µν ∂µ φa ∂ν φb − V (φ)
                                 2
                                                                Outline

                                                                When UV physics
    The fields φa coordinatize some field manifold M with         does not decouple
                                                                Our highest energy
                     1
    connection Γa = 2 γ ad (∂b γdc + ∂c γbd − ∂d γbc )
                bc
                                                                probe?
                                                                Probing
                                                                compactifications?
    And the associated Riemann tensor:                          Inflation with a
    Ra bcd = ∂c Γa − ∂d Γa + Γa Γe − Γa Γe
                 bd      bc   ce db    de cb
                                                                mass hierarchy
                                                                Bends in field space
                                                                Features in the power
    The equations of motion are given by                        spectrum

     φa + Γa g µν ∂µ φb ∂ν φc = ∂V /∂φa
           bc
    We note that we can associate an energy scale
    associated with the curvature of M : R ∼ Λ−2 .
                                               M
    In many concrete settings such as modular sector of
    string compactifications: ΛM ∼ Mstring
                                                               Features of string
Non decoupling of heavy directions?                           scale physics in the
                                                                     CMB
The inflaton trajectory is then determined by the forcing of    Subodh P. Patil

the steepest descent directions of V on the span of           Introductory
geodesics of γab .                                            remarks
                                                              Priors and
                                                              degeneracies
    If the inflaton traverses a sharp enough bend in field      Biases in our priors?
                                                              Outline
    space (without interrupting slow-roll), one can imagine   When UV physics
    exciting the heavy directions                             does not decouple
                                                              Our highest energy
                                                              probe?
                                                              Probing
                                                              compactifications?

                                                              Inflation with a
                                                              mass hierarchy
                                                              Bends in field space
                                                              Features in the power
                                                              spectrum
                                                              Features of string
Non-decouling of heavy directions?                           scale physics in the
                                                                    CMB

                                                              Subodh P. Patil
Evidently, it is possible to violate the adiabatic
approximation whilst preserving slow roll inflation.          Introductory
                                                             remarks
                                                             Priors and
    As heavy quanta are created in traversing sharp enough   degeneracies
                                                             Biases in our priors?
    features, the perturbations of the inflaton (the light)   Outline

    direction scatter off these heavy quanta                  When UV physics
                                                             does not decouple
                                                             Our highest energy
                                                             probe?
                                                             Probing
                                                             compactifications?

                                                             Inflation with a
                                                             mass hierarchy
                                                             Bends in field space
                                                             Features in the power
                                                             spectrum
                                                                Features of string
Non-decouling of heavy directions?                             scale physics in the
                                                                      CMB

                                                                Subodh P. Patil
Evidently, it is possible to violate the adiabatic
approximation whilst preserving slow roll inflation.            Introductory
                                                               remarks
                                                               Priors and
    As heavy quanta are created in traversing sharp enough     degeneracies
                                                               Biases in our priors?
    features, the perturbations of the inflaton (the light)     Outline

    direction scatter off these heavy quanta                    When UV physics
                                                               does not decouple
    Result in transient oscillations, damped by the dilution   Our highest energy
                                                               probe?
                                                               Probing
    of the heavy particles                                     compactifications?

                                                               Inflation with a
                                                               mass hierarchy
                                                               Bends in field space
                                                               Features in the power
                                                               spectrum
                                                                Features of string
Non-decouling of heavy directions?                             scale physics in the
                                                                      CMB

                                                                Subodh P. Patil
Evidently, it is possible to violate the adiabatic
approximation whilst preserving slow roll inflation.            Introductory
                                                               remarks
                                                               Priors and
    As heavy quanta are created in traversing sharp enough     degeneracies
                                                               Biases in our priors?
    features, the perturbations of the inflaton (the light)     Outline

    direction scatter off these heavy quanta                    When UV physics
                                                               does not decouple
    Result in transient oscillations, damped by the dilution   Our highest energy
                                                               probe?
                                                               Probing
    of the heavy particles                                     compactifications?

                                                               Inflation with a
    We will see that the violation of adiabaticity is          mass hierarchy
                                                               Bends in field space
    determined by the departure from unity of the quantity     Features in the power
                 ˙                   ˙
    e β = 1 + 4φ2 /(κ2 M 2 ) , where φ0 is the background
                                                               spectrum
                   0
    inflaton velocity κ is the radius of curvature of the
    trajectory in field space and M is the mass of the heavy
    direction.
                                                                Features of string
Non-decouling of heavy directions?                             scale physics in the
                                                                      CMB

                                                                Subodh P. Patil
Evidently, it is possible to violate the adiabatic
approximation whilst preserving slow roll inflation.            Introductory
                                                               remarks
                                                               Priors and
    As heavy quanta are created in traversing sharp enough     degeneracies
                                                               Biases in our priors?
    features, the perturbations of the inflaton (the light)     Outline

    direction scatter off these heavy quanta                    When UV physics
                                                               does not decouple
    Result in transient oscillations, damped by the dilution   Our highest energy
                                                               probe?
                                                               Probing
    of the heavy particles                                     compactifications?

                                                               Inflation with a
    We will see that the violation of adiabaticity is          mass hierarchy
                                                               Bends in field space
    determined by the departure from unity of the quantity     Features in the power
                 ˙                   ˙
    e β = 1 + 4φ2 /(κ2 M 2 ) , where φ0 is the background
                                                               spectrum
                   0
    inflaton velocity κ is the radius of curvature of the
    trajectory in field space and M is the mass of the heavy
    direction.
    Results in a modified speed of sound cs = e −β for the
                                          2

    propagation of the curvature perturbations.
                                                                     Features of string
Perturbations                                                       scale physics in the
                                                                           CMB
We now consider perturbations around a background solution           Subodh P. Patil
φa (τ, x) = φa (τ ) + δφa (τ, x) , with a perturbed line element
               0
                                                                    Introductory
ds 2 = a2 (τ )[−dτ 2 (1 + 2ψ(τ, x)) + (1 − 2ψ(τ, x))dx i dx i ] .   remarks
                                                                    Priors and
     Expanding the gravitational and scalar field action to          degeneracies
                                                                    Biases in our priors?
     second order, we express perturbations in terms of the         Outline

                                                                    When UV physics
     (gauge invariant) ‘Mukhanov-Sasaki’ variables:                 does not decouple
                       a
     v a ≡ a[δφa + φτ ψ] , to obtain the equations of motion:
                      H
                                                                    Our highest energy
                                                                    probe?
                                                                    Probing
                                                                    compactifications?

                                                                    Inflation with a
                                                                    mass hierarchy
                                                                    Bends in field space
                                                                    Features in the power
                                                                    spectrum
                                                                           Features of string
Perturbations                                                             scale physics in the
                                                                                 CMB
We now consider perturbations around a background solution                 Subodh P. Patil
φa (τ, x) = φa (τ ) + δφa (τ, x) , with a perturbed line element
               0
                                                                          Introductory
ds 2 = a2 (τ )[−dτ 2 (1 + 2ψ(τ, x)) + (1 − 2ψ(τ, x))dx i dx i ] .         remarks
                                                                          Priors and
     Expanding the gravitational and scalar field action to                degeneracies
                                                                          Biases in our priors?
     second order, we express perturbations in terms of the               Outline

                                                                          When UV physics
     (gauge invariant) ‘Mukhanov-Sasaki’ variables:                       does not decouple
                       a
     v a ≡ a[δφa + φτ ψ] , to obtain the equations of motion:
                      H
                                                                          Our highest energy
                                                                          probe?
                                                                          Probing
                                                                          compactifications?
          T
     d 2 vα          N
              + 2ζ dvα − ζ 2 vα +
                              T     dζ N                                  Inflation with a
      dτ 2          dτ              dτ vα
                                                   N                T
                                            + ΩTN vα + (ΩTT + k 2 )vα = 0 hierarchy
                                                                      mass
          N
     d 2 vα          T                                                    Bends in field space

      dτ 2
              − 2ζ dvα − ζ 2 vα −
                    dτ
                              N     dζ T
                                    dτ vα
                                                   T                N Features
                                            + ΩNT vα + (ΩNN + k 2 )vα = 0 in the power
                                                                       spectrum
                                                                           Features of string
Perturbations                                                             scale physics in the
                                                                                 CMB
We now consider perturbations around a background solution                 Subodh P. Patil
φa (τ, x) = φa (τ ) + δφa (τ, x) , with a perturbed line element
               0
                                                                          Introductory
ds 2 = a2 (τ )[−dτ 2 (1 + 2ψ(τ, x)) + (1 − 2ψ(τ, x))dx i dx i ] .         remarks
                                                                          Priors and
     Expanding the gravitational and scalar field action to                degeneracies
                                                                          Biases in our priors?
     second order, we express perturbations in terms of the               Outline

                                                                          When UV physics
     (gauge invariant) ‘Mukhanov-Sasaki’ variables:                       does not decouple
                       a
     v a ≡ a[δφa + φτ ψ] , to obtain the equations of motion:
                      H
                                                                          Our highest energy
                                                                          probe?
                                                                          Probing
                                                                          compactifications?
          T
     d 2 vα          N
              + 2ζ dvα − ζ 2 vα +
                              T     dζ N                                  Inflation with a
      dτ 2          dτ              dτ vα
                                                   N                T
                                            + ΩTN vα + (ΩTT + k 2 )vα = 0 hierarchy
                                                                      mass
          N
     d 2 vα          T                                                    Bends in field space
         − 2ζ dvα − ζ 2 vα −
      dτ 2     dτ
                         N          dζ T                    N Features
                                    + ΩNT vα + (ΩNN + k 2 )vα = 0 in the power
                                    dτ vα
                                             T
                                                               spectrum

     With the generalization of the slow roll parameters:
           H   ˙      ˙
                      φ2                               ˙
                                                     D φa
       ≡ − H2 =       2
                        0
                    2MPl H 2
                               and η a ≡ − H1˙
                                            φ         dt
                                                         0
                                                 0
                                                                           Features of string
Perturbations                                                             scale physics in the
                                                                                 CMB
We now consider perturbations around a background solution                 Subodh P. Patil
φa (τ, x) = φa (τ ) + δφa (τ, x) , with a perturbed line element
               0
                                                                          Introductory
ds 2 = a2 (τ )[−dτ 2 (1 + 2ψ(τ, x)) + (1 − 2ψ(τ, x))dx i dx i ] .         remarks
                                                                          Priors and
     Expanding the gravitational and scalar field action to                degeneracies
                                                                          Biases in our priors?
     second order, we express perturbations in terms of the               Outline

                                                                          When UV physics
     (gauge invariant) ‘Mukhanov-Sasaki’ variables:                       does not decouple
                       a
     v a ≡ a[δφa + φτ ψ] , to obtain the equations of motion:
                      H
                                                                          Our highest energy
                                                                          probe?
                                                                          Probing
                                                                          compactifications?
          T
     d 2 vα          N
              + 2ζ dvα − ζ 2 vα +
                              T     dζ N                                  Inflation with a
      dτ 2          dτ              dτ vα
                                                   N                T
                                            + ΩTN vα + (ΩTT + k 2 )vα = 0 hierarchy
                                                                      mass
          N
     d 2 vα          T                                                    Bends in field space
         − 2ζ dvα − ζ 2 vα −
      dτ 2     dτ
                         N          dζ T                    N Features
                                    + ΩNT vα + (ΩNN + k 2 )vα = 0 in the power
                                    dτ vα
                                             T
                                                               spectrum

     With the generalization of the slow roll parameters:
           H   ˙      ˙
                      φ2                               ˙
                                                     D φa
       ≡ − H2 =       2
                        0
                    2MPl H 2
                               and η a ≡ − H1˙
                                            φ         dt
                                                         0
                                                 0

     With ζ ≡ ZTN = aHη⊥ ,
                                                           2
     ΩTT = −a2 H 2 2 + 2 − 3η|| + η|| ξ|| − 4 η|| + 2 2 − η⊥ ,
     ΩNN = −a  2 H 2 (2 − ) + a2 M 2 ,
                                                      ˙
                                                     η⊥
     ΩTN = a2 H 2 η⊥ (3 + − 2η|| − ξ⊥ ) and ξ⊥ ≡ − Hη⊥ .
                                                                                        Features of string
Effective theory for the adiabatic mode                                                 scale physics in the
                                                                                              CMB

Given that ΩNN      |ΩTT | and ΩNN    |ΩTN | the field v N is                            Subodh P. Patil

the heavier of the two. We noting that the above equations                             Introductory
                                                                                       remarks
can be derived from the action:                                                        Priors and
                                                                                       degeneracies
                                                                                       Biases in our priors?
                                                                                       Outline
                                       2                2                          2
                        1      dv T
    S=      dτ d 3 x    2       dτ         −    vT          − ΩTT − ζ 2    vT          When UV physics
                                                                                       does not decouple
                                                                                       Our highest energy
                                   2                2                          2       probe?
                    1       dv N
    +    dτ d 3 x   2        dτ        −       vN       − ΩNN − ζ 2       vN           Probing
                                                                                       compactifications?

                                                                                       Inflation with a
                                       dζ        d
    −    dτ d 3 x v N ΩTN −            dτ   − 2ζ dτ v T                                mass hierarchy
                                                                                       Bends in field space
                                                                                       Features in the power
                                                                                       spectrum
                                                                                           Features of string
Effective theory for the adiabatic mode                                                    scale physics in the
                                                                                                 CMB

Given that ΩNN      |ΩTT | and ΩNN    |ΩTN | the field v N is                               Subodh P. Patil

the heavier of the two. We noting that the above equations                                Introductory
                                                                                          remarks
can be derived from the action:                                                           Priors and
                                                                                          degeneracies
                                                                                          Biases in our priors?
                                                                                          Outline
                                        2                  2                          2
                        1      dv T
    S=      dτ d 3 x    2       dτ           −      vT         − ΩTT − ζ 2    vT          When UV physics
                                                                                          does not decouple
                                                                                          Our highest energy
                                    2                  2                          2       probe?
                    1       dv N
    +    dτ d 3 x   2        dτ         −         vN       − ΩNN − ζ 2       vN           Probing
                                                                                          compactifications?

                                                                                          Inflation with a
                                            dζ        d
    −    dτ d 3 x v N ΩTN −                 dτ   − 2ζ dτ v T                              mass hierarchy
                                                                                          Bends in field space
                                                                                          Features in the power
    We can integrate out the                 vN   to leading order to obtain              spectrum


    the effective action
                                        2
                               dϕ
    S=      dτ d 3 k    1
                        2      dτ           − ϕ e −β(τ,k) k 2 ϕ − ϕ Ω(τ, k)ϕ
                                                                                                   Features of string
Effective theory for the adiabatic mode                                                            scale physics in the
                                                                                                         CMB

Given that ΩNN      |ΩTT | and ΩNN    |ΩTN | the field v N is                                       Subodh P. Patil

the heavier of the two. We noting that the above equations                                        Introductory
                                                                                                  remarks
can be derived from the action:                                                                   Priors and
                                                                                                  degeneracies
                                                                                                  Biases in our priors?
                                                                                                  Outline
                                              2                  2                            2
                              1      dv T
    S=             dτ d 3 x   2       dτ           −      vT         − ΩTT − ζ 2      vT          When UV physics
                                                                                                  does not decouple
                                                                                                  Our highest energy
                                          2                  2                            2       probe?
                         1        dv N
    +     dτ d 3 x       2         dτ         −         vN       − ΩNN − ζ 2         vN           Probing
                                                                                                  compactifications?

                                                                                                  Inflation with a
                                                  dζ        d
    −     dτ d 3 x v N ΩTN −                      dτ   − 2ζ dτ v T                                mass hierarchy
                                                                                                  Bends in field space
                                                                                                  Features in the power
    We can integrate out the                       vN   to leading order to obtain                spectrum


    the effective action
                                              2
                                     dϕ
    S=             dτ d 3 k   1
                              2      dτ           − ϕ e −β(τ,k) k 2 ϕ − ϕ Ω(τ, k)ϕ

    with ϕ ≡ e β/2 v T , and
                                                                                −1
              2)                         M2                             k2
    e β(τ,k                2
                   ≡ 1 + 4η⊥             H2
                                                       2
                                              − 2 + − η⊥ +             a2 H 2
                                                                Features of string
Numerics                                                       scale physics in the
                                                                      CMB

                                                                Subodh P. Patil

                                                               Introductory
                                                               remarks
                                                               Priors and
                                                               degeneracies
                                                               Biases in our priors?
We numerically evaluate the power spectrum from the full       Outline

coupled equations, and from the effective theory. We            When UV physics
                                                               does not decouple
evaluate the resulting power spectrum from a single sudden     Our highest energy
                                                               probe?
bend in field space preserving slow roll. We pick a fiducial     Probing
                                                               compactifications?

background solution which renders the attractor values         Inflation with a
                                                               mass hierarchy
  = 0.022, η|| = 0.034 in the absence of any bending in field   Bends in field space
                                                               Features in the power
space. N.B. in what follows, we have COBE normalized at        spectrum

the pivot scale k∗ = 0.002Mpc −1 .
                                                                  Features of string
                                                                 scale physics in the
                                                                        CMB

                                                                  Subodh P. Patil
     1.4
                                                                 Introductory
                                                                 remarks
     1.2                                                         Priors and
                                                                 degeneracies
                                                                 Biases in our priors?
                                                                 Outline
     1.0
                                                                 When UV physics
                                                                 does not decouple
                                                                 Our highest energy
     0.8                                                         probe?
PR




                                                                 Probing
                                                                 compactifications?

     0.6                                                         Inflation with a
                                                                 mass hierarchy
                                                                 Bends in field space
                                                                 Features in the power
     0.4                                                         spectrum

               Η   0
     0.2


     0.0
       0.002       0.005   0.010         0.020   0.050   0.100
                                         1
                                   Mpc
                                                                          Features of string
                                                                         scale physics in the
                                                                                CMB

                                                                          Subodh P. Patil
     1.4
                                                                         Introductory
                                                                         remarks
     1.2                                                                 Priors and
                                                                         degeneracies
                                                                         Biases in our priors?
                                                                         Outline
     1.0
                                                                         When UV physics
                                                                         does not decouple
                                                                         Our highest energy
     0.8                                                                 probe?
PR




                                                                         Probing
                                                                         compactifications?

     0.6                                                                 Inflation with a
                                                                         mass hierarchy
                                                                         Bends in field space

     0.4       Η     2                                                   Features in the power
                                                                         spectrum
                   N 0.25
     0.2       M2 H2         300

     0.0
       0.002         0.005         0.010         0.020   0.050   0.100
                                                 1
                                           Mpc
                                                                          Features of string
                                                                         scale physics in the
                                                                                CMB

                                                                          Subodh P. Patil
     1.4
                                                                         Introductory
                                                                         remarks
     1.2                                                                 Priors and
                                                                         degeneracies
                                                                         Biases in our priors?
                                                                         Outline
     1.0
                                                                         When UV physics
                                                                         does not decouple
                                                                         Our highest energy
     0.8                                                                 probe?
PR




                                                                         Probing
                                                                         compactifications?

     0.6                                                                 Inflation with a
                                                                         mass hierarchy
                                                                         Bends in field space

     0.4       Η     5                                                   Features in the power
                                                                         spectrum
                   N 0.25
     0.2       M2 H2         300

     0.0
       0.002         0.005         0.010         0.020   0.050   0.100
                                                 1
                                           Mpc
                                                                          Features of string
                                                                         scale physics in the
                                                                                CMB

                                                                          Subodh P. Patil
     1.4
                                                                         Introductory
                                                                         remarks
     1.2                                                                 Priors and
                                                                         degeneracies
                                                                         Biases in our priors?
                                                                         Outline
     1.0
                                                                         When UV physics
                                                                         does not decouple
                                                                         Our highest energy
     0.8                                                                 probe?
PR




                                                                         Probing
                                                                         compactifications?

     0.6                                                                 Inflation with a
                                                                         mass hierarchy
                                                                         Bends in field space

     0.4       Η     5                                                   Features in the power
                                                                         spectrum
                   N 0.5
     0.2       M2 H2         300

     0.0
       0.002         0.005         0.010         0.020   0.050   0.100
                                                 1
                                           Mpc
                                                                          Features of string
                                                                         scale physics in the
                                                                                CMB

                                                                          Subodh P. Patil
     1.4
                                                                         Introductory
                                                                         remarks
     1.2                                                                 Priors and
                                                                         degeneracies
                                                                         Biases in our priors?
                                                                         Outline
     1.0
                                                                         When UV physics
                                                                         does not decouple
                                                                         Our highest energy
     0.8                                                                 probe?
PR




                                                                         Probing
                                                                         compactifications?

     0.6                                                                 Inflation with a
                                                                         mass hierarchy
                                                                         Bends in field space

     0.4       Η     2                                                   Features in the power
                                                                         spectrum
                   N 0.25
     0.2       M2 H2         100

     0.0
       0.002         0.005         0.010         0.020   0.050   0.100
                                                 1
                                           Mpc
                                                                        Features of string
                                                                       scale physics in the
                                                                              CMB

                                                                        Subodh P. Patil
     1.4
                                                                       Introductory
                                                                       remarks
     1.2                                                               Priors and
                                                                       degeneracies
                                                                       Biases in our priors?
                                                                       Outline
     1.0
                                                                       When UV physics
                                                                       does not decouple
                                                                       Our highest energy
     0.8                                                               probe?
PR




                                                                       Probing
                                                                       compactifications?

     0.6                                                               Inflation with a
                                                                       mass hierarchy
                                                                       Bends in field space

     0.4       Η     2                                                 Features in the power
                                                                       spectrum
                   N 0.25
     0.2       M2 H2        50

     0.0
       0.002        0.005        0.010         0.020   0.050   0.100
                                               1
                                         Mpc
                                                            Features of string
A toy model                                                scale physics in the
                                                                  CMB

                                                            Subodh P. Patil

                                                           Introductory
We now explore a concrete model that generates the         remarks
                                                           Priors and
requisite functional behaviour for η⊥ and the slow roll    degeneracies
                                                           Biases in our priors?
parameters. Consider the two field model with the fields     Outline


φ1 = χ, φ2 = Ψ , and the sigma model metric:               When UV physics
                                                           does not decouple
                                                           Our highest energy
                 1    Γ(χ)                                 probe?
     γab =                    , with Γ2 (χ) < 1            Probing
               Γ(χ)    1                                   compactifications?

                                                           Inflation with a
     We consider the separable potential                   mass hierarchy

     V (χ, ψ) = V0 (χ) + 1 M 2 ψ 2
                                                           Bends in field space
                                                           Features in the power
                          2                                spectrum
                            Γ0
    With Γ(χ) =   cosh2 [2(χ−χ0 )/∆χ]
    Again, we pick V0 (χ) to render the attractor values
     = 0.022, η|| = 0.034 in the absence of any bends
                                                                Features of string
                                                               scale physics in the
    2                                                                 CMB

                                                                Subodh P. Patil

                                                               Introductory
                                                               remarks
                                                               Priors and
    1                                                          degeneracies
                                                               Biases in our priors?
                                                               Outline

                                                               When UV physics
                                                               does not decouple
                                                               Our highest energy
    0                                                          probe?
Η




                                                               Probing
                                                               compactifications?

                                                               Inflation with a
                                                               mass hierarchy
                                            Χ 0.076 MPl        Bends in field space
                                                               Features in the power
    1                                       0 0.9              spectrum


                                           M2 H2   300


    2
        1          0             1            2            3
                                N

Solid line = η⊥ , dashed line = 10 × η|| as functions of
e -fold number N
                                                               Features of string
                                                              scale physics in the
                                                                     CMB

                                                               Subodh P. Patil
     1.4
                                                              Introductory
                                                              remarks
     1.2                                                      Priors and
                                                              degeneracies
                                                              Biases in our priors?
                                                              Outline
     1.0
                                                              When UV physics
                                                              does not decouple
                                                              Our highest energy
     0.8                                                      probe?
PR




                                                              Probing
                                                              compactifications?

     0.6                                                      Inflation with a
                                                              mass hierarchy
                                                              Bends in field space
                                                              Features in the power
     0.4                                                      spectrum



     0.2


     0.0
        0.002   0.005   0.010         0.020   0.050   0.100
                                      1
                                Mpc
                                                                Features of string
                                                               scale physics in the
    4                                                                 CMB

                                                                Subodh P. Patil

                                                               Introductory
                                                               remarks
                                                               Priors and
    2                                                          degeneracies
                                                               Biases in our priors?
                                                               Outline

                                                               When UV physics
                                                               does not decouple
                                                               Our highest energy
    0                                                          probe?
Η




                                                               Probing
                                                               compactifications?

                                                               Inflation with a
                                                               mass hierarchy
                                            Χ 0.041 MPl        Bends in field space
                                                               Features in the power
    2                                       0 0.9              spectrum


                                           M2 H2   300


    4
        1          0             1            2            3
                                N

Solid line = η⊥ , dashed line = 10 × η|| as functions of
e -fold number N
                                                               Features of string
                                                              scale physics in the
                                                                     CMB

                                                               Subodh P. Patil
     1.4
                                                              Introductory
                                                              remarks
     1.2                                                      Priors and
                                                              degeneracies
                                                              Biases in our priors?
                                                              Outline
     1.0
                                                              When UV physics
                                                              does not decouple
                                                              Our highest energy
     0.8                                                      probe?
PR




                                                              Probing
                                                              compactifications?

     0.6                                                      Inflation with a
                                                              mass hierarchy
                                                              Bends in field space
                                                              Features in the power
     0.4                                                      spectrum



     0.2


     0.0
        0.002   0.005   0.010         0.020   0.050   0.100
                                      1
                                Mpc
                                                               Features of string
Discussion                                                    scale physics in the
                                                                     CMB

                                                               Subodh P. Patil

As advertised, very prominent oscillatory features present.   Introductory

Could such a primordial spectrum off a better (e.g. χ2 ) fit    remarks
                                                              Priors and
                                                              degeneracies
to the data?                                                  Biases in our priors?
                                                              Outline
    As advertised, effective field theory manifests for the     When UV physics
                                                              does not decouple
    longest wavelengths, a reduced speed of sound.            Our highest energy
                                                              probe?
                                                              Probing
                                                              compactifications?

                                                              Inflation with a
                                                              mass hierarchy
                                                              Bends in field space
                                                              Features in the power
                                                              spectrum
                                                               Features of string
Discussion                                                    scale physics in the
                                                                     CMB

                                                               Subodh P. Patil

As advertised, very prominent oscillatory features present.   Introductory

Could such a primordial spectrum off a better (e.g. χ2 ) fit    remarks
                                                              Priors and
                                                              degeneracies
to the data?                                                  Biases in our priors?
                                                              Outline
    As advertised, effective field theory manifests for the     When UV physics
                                                              does not decouple
    longest wavelengths, a reduced speed of sound.            Our highest energy
                                                              probe?
    Thus we expect correlated (equilateral)                   Probing
                                                              compactifications?
    non-gaussianities                                         Inflation with a
                                                              mass hierarchy
                                                              Bends in field space
                                                              Features in the power
                                                              spectrum
                                                               Features of string
Discussion                                                    scale physics in the
                                                                     CMB

                                                               Subodh P. Patil

As advertised, very prominent oscillatory features present.   Introductory

Could such a primordial spectrum off a better (e.g. χ2 ) fit    remarks
                                                              Priors and
                                                              degeneracies
to the data?                                                  Biases in our priors?
                                                              Outline
    As advertised, effective field theory manifests for the     When UV physics
                                                              does not decouple
    longest wavelengths, a reduced speed of sound.            Our highest energy
                                                              probe?
    Thus we expect correlated (equilateral)                   Probing
                                                              compactifications?
    non-gaussianities                                         Inflation with a
                                                              mass hierarchy
    In principle, such superimposed oscillations offer us a    Bends in field space
                                                              Features in the power
    primitive spectroscopy.                                   spectrum
                                                                   Features of string
Discussion                                                        scale physics in the
                                                                         CMB

                                                                   Subodh P. Patil

As advertised, very prominent oscillatory features present.       Introductory

Could such a primordial spectrum off a better (e.g. χ2 ) fit        remarks
                                                                  Priors and
                                                                  degeneracies
to the data?                                                      Biases in our priors?
                                                                  Outline
    As advertised, effective field theory manifests for the         When UV physics
                                                                  does not decouple
    longest wavelengths, a reduced speed of sound.                Our highest energy
                                                                  probe?
    Thus we expect correlated (equilateral)                       Probing
                                                                  compactifications?
    non-gaussianities                                             Inflation with a
                                                                  mass hierarchy
    In principle, such superimposed oscillations offer us a        Bends in field space
                                                                  Features in the power
    primitive spectroscopy.                                       spectrum


    In combination with other statistics, might help us
    better infer the universality class of effective lagrangians
    that resulted in inflation.
                                                                   Features of string
Discussion                                                        scale physics in the
                                                                         CMB

                                                                   Subodh P. Patil

As advertised, very prominent oscillatory features present.       Introductory

Could such a primordial spectrum off a better (e.g. χ2 ) fit        remarks
                                                                  Priors and
                                                                  degeneracies
to the data?                                                      Biases in our priors?
                                                                  Outline
    As advertised, effective field theory manifests for the         When UV physics
                                                                  does not decouple
    longest wavelengths, a reduced speed of sound.                Our highest energy
                                                                  probe?
    Thus we expect correlated (equilateral)                       Probing
                                                                  compactifications?
    non-gaussianities                                             Inflation with a
                                                                  mass hierarchy
    In principle, such superimposed oscillations offer us a        Bends in field space
                                                                  Features in the power
    primitive spectroscopy.                                       spectrum


    In combination with other statistics, might help us
    better infer the universality class of effective lagrangians
    that resulted in inflation.
    Much more quality data to come!

				
DOCUMENT INFO
Shared By:
Categories:
Stats:
views:3
posted:6/26/2011
language:English
pages:74