Detecting Chameleons in the Laboratory Collaboration with C. van de Bruck, A. C. Davis, D.Mota and D. Shaw. Cosmo 2007 hep-ph/0703243 arxiv:0707/2801

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

Cosmic Acceleration

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

Gravity Tests Fifth force experiments Equivalence principle

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

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

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)

Laboratory Experiments: Probing Scalar Fields?

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)

PVLAS: new results 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 ?

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.

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

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

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

Rotation

Ellipticity

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

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.

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

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.