1. Detecting Chameleons in the Laboratory
Collaboration with C. van de Bruck, A. C. Davis, D.Mota and D. Shaw.
Cosmo 2007
hep-ph/
arxiv:0707/2801

2. Outline Chameleon Fields Gravity and miscellaneous tests
PVLAS, CAST and the Chameleon

3. Cosmic Acceleration

4. Nearly Massless Fields
very fast roll
implies that
indistinguishable from a cosmological constant
If then
Nearly massless field
Leads to strong gravitational constraints

5. Gravity Tests
Fifth force experiments
Equivalence principle

6. Effective field theories with gravity and scalars
coupling constant to matter
gravitational coupling constant:
Geodesics deviate from general relativity

7. Chameleon Fields
When coupled to matter, moduli have matter dependent effective potential
In cosmology
coupling to nonrelativistic matter only

8. Typical example:
Ratra-Peebles potential
Constant coupling to matter

9. 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)

10. Laboratory Experiments: Probing Scalar Fields?

11. The original PVLAS experiment 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 effect)
The phenomenon could 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)

13. PVLAS: new results
New runs looking for experimental artifacts have contradicted the 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).

14. 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 ?

15. The energy density depends on the magnetic field:
The mass of the chameleon is given by:
No chameleon production in the sun if massive enough:
For a density the mass in the sun is:
Hence chameleons evade the CAST bound.

16. Testing Chameleons Gravitational tests: earth: solar system:
Cosmology:
modification of growth factor at short
distance:
cosmological variation of the fine structure
constant

17. One might wonder if the chameleon affected precision
experiments like the anomalous magnetic moment of the
muon via the interaction
When one evaluates the diagram, it is
which is much less than the direct
contribution. Other corrections
are smaller – eg to hyperfine splitting

18. 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

19. Rotation

20. Ellipticity

21. Predictions
Ellipticity always larger than rotation by a factor N (number of passes)

22. 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….
BMV (taking data now) should give us more clues.

23. Conclusions
Chameleon fields can reconcile quintessence and gravity experiments.
Will be tested soon via optical measurements.
Exciting time??

24. Radiative corrections
In the Einstein frame, below the electron mass, the effective theory obtained by integration out matter fields involves only photons and chameleons with a correction the scalar potential determined solely by covariance:
Fine tuning of the cosmological constant implies that the corrections to the mass of the chameleons are suppressed too.
In the Jordan frame, all radiative processes involving only standard model fields (not gravity) do not involve the chameleon at all. Hence the form of the coupling of the chameleon to matter is stable.