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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!

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