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Spherical Collapse in Chameleon Models

Spherical Collapse in Chameleon Models. Work done with Ph. Brax and D. Steer (JCAP 2010). Rogerio Rosenfeld Instituto de Física Teórica UNESP. 2nd Bethe Center Workshop Cosmology meets Particle Physics.

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Spherical Collapse in Chameleon Models

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  1. SphericalCollapse in ChameleonModels Work donewith Ph. Braxand D. Steer (JCAP 2010) RogerioRosenfeld Instituto de Física Teórica UNESP 2nd Bethe Center Workshop CosmologymeetsParticlePhysics

  2. Chameleon: scalarfieldwithenvironmentaldependentproperties(KhouryandWeltman 2004) General mechanism(Damouret al. 1990) Weylscalingofthemetric Jordan frame Einstein frame Massesandcouplingsbecomespace-timedependentin Einstein frame!

  3. Matterenergy-momentum tensor is notconserved in Einstein frame due to scalarfieldcoupling: Scalarfieldobeys a Klein-Gordon equationwithaneffectivepotential:

  4. Massofscalarfielddependsonthedarkmatterdensity: Relevant for mR<1 in order to modifytheevolutionofstructure. Chameleoncouplingchangesperturbedmetric: Matterfollowsaneffectivegravitationalperturbation:

  5. Modificationofgravity for a pointmassand V=0: Muststudychameleonprofile in sphericalstructureswithtime-dependentradiusanddensity

  6. For small bodies: similar to thepoint-likemass case. For largebodiesthefieldremainsconstant in aninnerregionofradius RSabovewhich it relaxes in a shell to the background valueresulting in:

  7. Theradius RS is determinedbythecontinuityofthefield in R and is givenby: and is model-dependent (dependsonthescalarpotential). Inverse-power-lawpotential:

  8. The usual newtonianpotentialgetsmodifiedby a factor (thinshelleffect) GR (b=0 or RS =R , g=1); small body (RS =0) Modifiedaccelerationequation: • Caveats (ok for thinshells): • densityremainsuniform • no shellcrssing

  9. Initialconditionschosen for collapsetoday in LCDM.

  10. Shellsdisappearquickly: Initialdensitycontrasts for chosen for collapsetoday

  11. Conclusions • Initialstudyontheinfluenceofchameleons in thenonlinear regime ofsphericalcollapse, includingthinshelleffect; • Collapsedependsonsizeofinitialperturbation; • Movingbarrierproblem for structureformation; • Mustunderstandfull dynamics beyondthesimpleapproximationusedhere: nonuniformdensities, shellcrossing, etc.

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