Detecting Chameleons in the Detecting Chameleons in the LaboratoryLaboratory

Collaboration with C. van de Collaboration with C. van de Bruck, A. C. Davis, D.Mota Bruck, A. C. Davis, D.Mota

and D. Shaw.and D. Shaw.

Cosmo 2007

hep-ph/0703243

arxiv:0707/2801

OutlineOutline

Chameleon FieldsChameleon Fields Gravity and miscellaneous testsGravity and miscellaneous tests PVLAS, CAST and the ChameleonPVLAS, CAST and the Chameleon

Cosmic AccelerationCosmic Acceleration

Nearly Massless FieldsNearly Massless Fields

very fast rollvery fast roll

implies that implies that

indistinguishable from a cosmological constantindistinguishable from a cosmological constant

If then If then

Nearly massless field Nearly massless field

Leads to Leads to strong gravitational constraintsstrong gravitational constraints

Gravity TestsGravity Tests

Fifth force experimentsFifth force experiments

Equivalence principleEquivalence principle

Effective field theories with gravity and scalarsEffective field theories with gravity and scalars

coupling constant to mattercoupling constant to matter

gravitational coupling constant:gravitational coupling constant:

Geodesics deviate from general relativityGeodesics deviate from general relativity

Chameleon FieldsChameleon Fields When coupled to matter, moduli have matter dependent effective When coupled to matter, moduli have matter dependent effective

potentialpotential

In cosmologyIn cosmology

coupling to nonrelativistic matter onlycoupling 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 Laboratory Experiments: Probing Scalar Fields?Scalar Fields?

The original PVLAS experiment claimed to have observed a signal for The original PVLAS experiment claimed to have observed a signal for the the birefrigencebirefrigence (ellipticity) and the (ellipticity) and the dichroism dichroism (rotation) of a polarised (rotation) of a polarised laser beam going through a static magnetic field.laser beam going through a static magnetic field.

Effect claimed to be larger than induced by higher order terms in the Effect claimed to be larger than induced by higher order terms in the QED Lagrangian (one loop) or gaseous effects (Cotton-Mouton effect)QED Lagrangian (one loop) or gaseous effects (Cotton-Mouton effect)

The phenomenon could be interpreted as a result of the The phenomenon could be interpreted as a result of the mixingmixing between between photonsphotons and and scalarsscalars..

More precisely: a coupling between 2 photons and a scalar can induce More precisely: a coupling between 2 photons and a scalar can induce two effects:two effects:

RotationRotation: a photon can be transformed in a scalar.: a photon can be transformed in a scalar.

EllipticityEllipticity: a photon can be transformed into a scalar and then : a photon can be transformed into a scalar and then regenerated as a photon (delay)regenerated as a photon (delay)

PVLAS: new resultsPVLAS: new results

New runs looking for experimental artifacts have New runs looking for experimental artifacts have contradicted the 2000-2005 experimental results.contradicted the 2000-2005 experimental results.

No rotation signal observed at 2.3 T and 5.5 TNo rotation signal observed at 2.3 T and 5.5 T No ellipticity signal at 2.3 T and a large positive signal at No ellipticity signal at 2.3 T and a large positive signal at

5.5 T5.5 T

Ellipticity incompatible with a traditional scalar/axion Ellipticity incompatible with a traditional scalar/axion interpretation ( scaling).interpretation ( scaling).

PVLAS vs CASTPVLAS vs CAST

Putative PVLAS experimental results could be seen as a Putative PVLAS experimental results could be seen as a result of the coupling:result of the coupling:

Limits on mass of scalar quite stringent:Limits on mass of scalar quite stringent:

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

What if ? What if ? CHAMELEON ?CHAMELEON ?

The energy density depends on the magnetic field:The energy density depends on the magnetic field:

The mass of the chameleon is given by:The mass of the chameleon is given by:

No chameleon production in the sun if massive enough:No chameleon production in the sun if massive enough:

For a density the mass in the sun is:For a density the mass in the sun is:

Hence Hence chameleons evade the CAST boundchameleons evade the CAST bound..

Testing ChameleonsTesting Chameleons Gravitational testsGravitational tests::

earth:earth:

solar system: solar system:

CosmologyCosmology::

modification of growth factor at short modification of growth factor at short distance:distance:

cosmological variation of the fine structurecosmological variation of the fine structure constantconstant

One might wonder if the chameleon affected precisionOne might wonder if the chameleon affected precisionexperiments like the experiments like the anomalous magnetic moment of the anomalous magnetic moment of the muonmuon via the interaction via the interaction

When one evaluates the diagram, it isWhen one evaluates the diagram, it is

which is much less than the direct which is much less than the direct contribution. Other correctionscontribution. Other correctionsare smaller – eg to are smaller – eg to hyperfine splittinghyperfine splitting

Chameleon OpticsChameleon Optics

Chameleons never leave Chameleons never leave the cavity (outside mass the cavity (outside mass too large, no tunnelling)too large, no tunnelling)

Chameleons do not reflect Chameleons do not reflect simultaneously with simultaneously with photons.photons.

Chameleons propagate Chameleons propagate slower in the no-field zone slower in the no-field zone within the cavitywithin the cavity

RotationRotation

EllipticityEllipticity

PredictionsPredictions

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

Can fit the new data with various values of n Can fit the new data with various values of n and M:and M:

We know that these parameters lead to a We know that these parameters lead to a full compatibility with gravity tests, full compatibility with gravity tests, cosmology, CAST….cosmology, CAST….

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

ConclusionsConclusions

Chameleon fields can reconcile Chameleon fields can reconcile quintessence and gravity experiments.quintessence and gravity experiments.

Will be tested soon via optical Will be tested soon via optical measurements.measurements.

Exciting time??Exciting time??

Radiative correctionsRadiative corrections

In the Einstein frame, below the electron mass, the In the Einstein frame, below the electron mass, the effective theory obtained by integration out matter fields effective theory obtained by integration out matter fields involves only photons and chameleons with a correction involves only photons and chameleons with a correction the scalar potential determined solely by covariance:the scalar potential determined solely by covariance:

Fine tuning of the cosmological constant implies that the Fine tuning of the cosmological constant implies that the corrections to the mass of the chameleons are suppressed corrections to the mass of the chameleons are suppressed too. too.

In the Jordan frame, all radiative processes involving only In the Jordan frame, all radiative processes involving only standard model fields (not gravity) do not involve the standard model fields (not gravity) do not involve the chameleon at all. Hence the form of the coupling of the chameleon at all. Hence the form of the coupling of the chameleon to matter is stable. chameleon to matter is stable.