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					           The Chameleon

 with P.Brax, C van deBruck,
    C.Burrage, J. Khoury,
A.Weltman,D.Mota, C.Shelpe,
    D. Seery and D.Shaw
     PRL 99(07)121103;
  0902.2320 +unpublished
•   Introduction to chameleon theories
•   Chameleon cosmology
•   Photon Coupling and PVLAS
•   Predictions + Casimir Force
•   Electroweak physics --Implications for LHC
•   Possible detection in AGNs + polarised starlight
•   Conclusions
The Big Puzzle
Equ of state
Consider scalar field

  potential dominated for

                Dark Energy?
 Like during primordial
inflation, scalar fields can
trigger the late acceleration
of the universe.

An attractive possibility:
runaway behaviour.

 The mass of the field now is
of order of the Hubble rate.
Almost massless.
   Do Scalars Couple to Matter?

    Effective field theories with gravity and

  deviation from Newton’s law
                The radion
The distance between branes in the Randall-Sundrum model:


 Deviations from Newton’s law

 Far away branes                small deviations

 close branes

 constant coupling constant
Experimental consequences?
Long lived scalar fields which couple with
ordinary matter lead to the presence of a new
Yukawa interaction:

  This new force would have gravitational effects
on the motion of planets, the laboratory tests of
gravity etc..
  The Chameleon Mechanism

When coupled to matter, scalar fields
have a matter dependent effective
Typical example:

    Ratra-Peebles potential

    Constant coupling to matter
Chameleon field: field with a matter dependent mass

A way to reconcile gravity tests and cosmology:

 Nearly massless field on cosmological scales

Massive field in the atmosphere

 Allow large gravitational coupling constant of order one or more

 Possible non-trivial effects in the solar system (satellite experiments)
                Gravity Tests
• Fifth force

• Equivalence principle
                   The thin-shell property
     • The chameleon force produced by a massive
       body is due only to a thin shell near the surface

     • Thin shell
          – deviations from Newton’s
     • Thick shell
          – deviations from Newton’s law

Khoury & Weltman (2004)
    Chameleon Cosmology

     Attractor Solution
           follows the minimum of the effective potential
     In agreement with cosmological observations
      (Redshift of recombination, BBN) if:

     Equation of state
           early times
           late times
     The chameleon is a natural DE candidate!
Brax, van de Bruck, Davis, Khoury, Weltman (2004)
                     Scalar Optics
• The PVLAS experiment originally claimed to have observed a signal
  for the birefrigence (ellipticity) and the dichroism (rotation) of a
  polarised laser beam going through a static magnetic field.
• Effect claimed to be larger than induced by higher order terms in the
  QED Lagrangian (one loop) or gaseous effects (Cotton-Mouton
• The phenomenon can be interpreted as a result of the mixing
  between photons and scalars.
• More precisely: a coupling between 2 photons and a scalar can
  induce two effects:
  Rotation: a photon can be transformed in a scalar.

   Ellipticity: a photon can be transformed into a scalar and then
   regenerated as a photon (delay)
                  PVLAS: Alas!
• New runs looking for experimental artifacts have
  contradicted the 2000-2005 experimental results.
• No rotation signal observed at 2.3 T and 5.5 T
• No ellipticity signal at 2.3 T and a large positive signal at
  5.5 T

• Ellipticity incompatible with a traditional scalar/axion
  interpretation (     scaling).
              PVLAS vs CAST
• Putative PVLAS experimental results could be seen as a
  result of the coupling:

• Limits on mass of scalar quite stringent:

• No contradiction with CAST experiments on scalar
  emitted from the sun

• What if                       ?

                       CHAMELEON ?
• Universality of coupling:

• Large gravitational coupling:

• No contradiction with gravity tests, variation of
  constants, cosmology, astrophysics bounds….
• No deviation from gravity in satellite
  experiments…. Small objects have a thin shell.
            Chameleon Optics
• Chameleons never leave
  the cavity (outside mass
  too large, no tunnelling)
• Chameleons do not
  reflect simultaneously
  with photons.
• Chameleons propagate
  slower in the no-field
  zone within the cavity
Predicted Rotation
Predicted Ellipticity
• Because the chameleon is reflected rather
   than escaping and their reflection is
   decoherent with photons we expect
•             ellipticity > rotation
  in chameleon theories. This is because, for
   a large number of passes in the chamber
   the ellipticity builds up but due to the
   decoherence the rotation doesn’t. At
   present we are in agreement with current
   experiments, but this could be tested
• Can fit the new data with various values of n
  and M:
• We know that these parameters lead to a
  full compatibility with gravity tests,
  cosmology, CAST….

• GammeV could see an `afterglow’
Casimir Force Experiments
 • Measure force between
  – Two parallel plates
    • Difficult to keep plates parallel
    •                           R. S. Decca et al., PRD 75 (2007)

  – A plate and a sphere
    • Harder to calculate analytically.
                                   S. K. Lamoreaux, PRL 78 (1997)

 • No physical shield is used.
  – Electrostatic forces calibrated for by
    controlling electric potential between plates.
      Chameleons & Casimir
• We consider two potentials:


• We find that currently:
What the future holds
          New experiments
• Two new experiments currently under
  construction have real prospect of
  detecting chameleons.

• Los Alamos experiment
 – Sphere and plate
 – Could detect chameleon force if
   without a detailed knowledge of the thermal
                                      S. K. Lamoreaux
• Next generation of Casimir force
  measurement experiments have the
  precision to detect almost all chameleon
  dark energy models with

• Generally a good model for the thermal
  Casimir force is required although some
  models can be detected without it.
Coupling to Electro-Weak Sector
 Chameleon can also couple to standard model particles. Would we see
    corrections in precision tests? Remember, chameleon mass small in expt
    vacuum pipe.

 o   Dark energy scalar like Higgs scalar: highly sensitive to high energy physics
     (UV completion)

 o   As Higgs mass taken to infinity, should recover divergences of SM without
     Higgs: quadratic divergences of self-energy. Higgs mass acts as a loose cut-
     off so in principle (Veltman param):

 o   Unfortunately it turns out that

 o   In principle same type of dependence for any scalar field:

 o                           Large corrections O(1)??
          Vacuum Polarisation

Daisies                                Bridges

                 Oblique Corrections
Effective Action and Couplings

The coupling involves two unknown coupling functions (gauge invariance):

 At one loop the relevant vertices are:
Self-Energy Corrections I

The corrected propagator becomes:

Measurements at low energy and the Z and W poles imply ten independent
quantities. Three have to be fixed experimentally. One is not detectable
hence six electroweak parameters: STUVWX
Self-Energy Corrections II
The self energy can be easily calculated:

The self energy parameters all involve quadratic divergences

For instance:

The quadratic divergences cancel in the precision tests:
     Dark Energy Screening
Vacuum Polarisation sensitive to the UV region of phase space
where the difference between the W and Z masses is negligible

Gauge invariance implies the existence of only two coupling
functions with no difference between the W and Z bosons in the
massless limit (compared to the UV region)

 No difference between the different particle vacuum
 polarisations, hence no effects on the precision tests.
       Experimental Constraints

                                  Stronger bound
                                  from optics! M
                                  greater than 1
                                  million GeV!

               Inverse Coupling
Rainbows, Daisies and Bridges

        Higher order corrections all suppressed
       ALPs and Dark Energy
Consider scalars and pseudoscalars coupling to
 photons through the terms

Such particles have been proposed as Dark
 Energy candidates:
  Coupled Quintessence    (Amendola 1999)
  Chameleon Dark Energy   (Khoury, Weltman 2004, Brax,
                           Davis, van de Bruck 2007 )
  Axionic Dark Energy     (Carroll 1998, Kim, Nilles 2003)
         ALPs and Dark Energy
We consider fields with
Pseudoscalars: limits from observations
 of neutrino burst from SN 1987A (Ellis, Olive
Scalars: limits from fifth force
Chameleons: limits from the structure of
 starlight polarisation
          Photon-ALP Mixing
Mixing when photons propagate through
 background magnetic fields
  Probability of mixing

Mixing with only one photon polarisation state
  Also induces polarisation
Strong Mixing limit:

                                     (Raffelt, Stodolsky 1987)
    Astrophysical Photon-ALP
Magnetic fields known to exist in
 galaxies/galaxy clusters
These magnetic fields made up of a large
 number of magnetic domains
  field in each domain of equal strength but
   randomly oriented
ALP mixing changes astrophysical
  Non-conservation of photon number alters
  Creation of polarisation
       Strong Mixing in Galaxy
Galaxy cluster:
  Magnetic field strength
  Magnetic coherence length
  Electron density
  Plasma frequency
  Typical no. domains traversed
Strong mixing if

     Effects of Strong Mixing on
After passing through many domains power is,
 on average, split equally between ALP and two
 polarisations of the photon
Average luminosity suppression = 2/3         (Csáki, Kaloper,
                                              Terning 2001)
Difficult to use this to constrain mixing because
 knowledge of initial luminosities is poor
Single source:

   If              ; averaged over many
        Active Galactic Nuclei
Strong correlation between 2 keV X-ray
 luminosity and optical luminosity (~5eV)
Use observations of 77 AGN from COMBO-17
 and ROSAT surveys (z=0.061-2.54) (Steffen et al. 2006)
Likelihood ratio
  r14          Assuming initial polarisation
  r>11          Allowing all polarisations

Is this really a preference for ALPsm? Or just an
 indication of more structure in the scatter?
105 bootstrap resamplings (with replacement) of
 the data - all samples 77 data points
Compute the central moments of the data

   is the standard deviation
      is the skewness of the data
Compare this with simulations of the best fit
 Gaussian and ALPsm models
              Conclusions I
• Chameleons automatically explain the observed
  acceleration of the universe.
• The could be detected by PVLAS experiments,
  evade the CAST bound and predict
• Casimir force experiments can test for
• The next generation of experiments could detect
  them or rule them out as dark energy
                Conclusions II

• Their coupling to matter is screened in
  precision tests of the electroweak
  physics due to UV sensitivity or vacuum
  polarisation and gauge invariance.
• Scatter in astrophysical luminosity
  relations can be used to study the
  mixing with photons in magnetic fields.
  Applied to AGN this shows strong
  evidence for chameleons/ALP strong
  mixing over Gaussian scatter.

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