Cosmological constraints on a dark matter -- dark

arXiv:astro-ph/0307350v226Aug2003Cosmologicalconstraintsonadarkmatter–darkenergyinteractionMarkB.Hoffman∗EnricoFermiInstitute,DepartmentofPhysics,andCenterforCosmologicalPhysicsUniversityofChicago5640S.EllisAvenue,Chicago,IL60637,USAFebruary2,2008AbstractItisgenerallyassumedthatthetwodarkcomponentsoftheenergydensityoftheuniverse,asmoothcomponentcalleddarkenergyandafluidofnonrelativisticweaklyinteractingparticlescalleddarkmatter,areindependentofeachotherandinteractonlythroughgravity.Inthispaper,weconsideraclassofmodelsinwhichthedarkmatteranddarkenergyinteractdirectly.Thedarkmatterparticlemassisproportionaltothevalueofascalarfield,andtheenergydensityofthisscalarfieldcomprisesthedarkenergy.WestudythephenomenologyofthesemodelsandcalculatetheluminositydistanceasafunctionofredshiftandtheCMBanisotropyspectrumforseveralcases.Wefindthatthephenomenologyofthesemodelscandiffersignificantlyfromthestandardcase,andcurrentobservationscanalreadyruleoutthesimplestmodels.∗[e-mail]11IntroductionPresentobservationsoftheuniversestronglysuggestthatroughlyninety-sixpercentoftheenergydensityoftheuniverseisduetoformsofmatterandenergythatarenotdescribedbythestandardmodelofparticlephysics.Theseformsofmatterandenergyhavelittleornodirectinteractionwithordinarymatter,andhencecannotbedirectlyobserved.Thedarksector,calledsuchbecauseitsenergyandmatterdonotemitlight,istypicallydividedintotwocategories,darkmatter,whichisclustered,anddarkenergy,whichissmoothlydistributedandpresentlycausingtheexpansionoftheuniversetoaccelerate.Itisalsogenerallyassumedthatthesetwocomponentsofthedarksectorareindependentanddonotinteractdirectly.However,therearenoexperimentsorobservationsthatareknowntoexplicitlyprecludesuchaninteraction.Thegoalofthisworkistoconductapreliminaryinvestigationintotheconstraintspresentobservationsplaceonpossibleinteractionsinthedarksector.Thoughtherearepresentlynodirectobservationsofthedarksector,thereareneverthe-lessmanyindirectmeasurementsthatgiveuscluesaboutitsnature.Measurementsoftherotationcurvesofspiralgalaxies,thetemperatureprofilesofgalaxyclusters,gravitationallensingofclusters,thelarge-scalemotionsofgalaxiesbetweenclusters,andapplyingthevirialtheoremtoclustersallrequireamassfortheseobjectsmuchlargerthanthatprovidedbytheluminousmatter[1,2,3,4,5].Itiswidelybelievedthattheextramassisprovidedbyafluidofnonrelativistic,weaklyinteractingparticlesknownascolddarkmatter(CDM).NumericalstudiesofstructureformationandcomparisontostatisticalstudiesofgalaxiesandclusterssupporttheCDMmodelonlargescales[6].Observationsoftheanisotropyspectrumofthecosmicmicrowavebackgroundradiation(CMB)[7,8,9]andthemagnitude-redshiftrelationforTypeIasupernovae(SNeIa)[10,11,12,13]indicatethepresenceofasecondcomponentofthedarksector,darkenergy,whichissmoothlydistributedandpresentlycausingtheexpansionoftheuniversetoaccelerate.ThelocationofthefirstacousticpeakoftheCMBanisotropyspectrumispredominantlygovernedbygeometryoftheuniverse,andhencethetotalenergydensityoftheuniverse.Themeasuredlocationofthefirstpeakimpliesthattheuniverseisverynearlyflat,i.e.Euclidean.However,themeasuredclusteredmatter,includingbothordinarymatteranddarkmatter,2onlycomprisesone-thirdoftheenergydensityrequiredforaflatuniverseimplyingtheexistenceofasmoothlydistributeddarkenergy.Measurementsofthemagnitude-redshiftrelationofSNeIaindicatethattheuniverserecentlyenteredaneraofacceleratedexpansion.Theamountofdarkenergyrequiredtocausetheobservedaccelerationalsomakesupfortherestoftheenergydensityneededtomaketheuniverseflat.Thesimplestexplanationforthedarkenergyisacosmologicalconstant,Λ(forreviewssee[14,15,16]).Thishypothesisfitsthedataextremelywellbutfacessignificanttheoreticalquestions.ThereisnoknownmechanismforproducingacosmologicalconstantassmallasisobservedwhencomparedwiththePlanckscale(Λ/M4P∼10−120),andthisconstantmustbeveryfinelytunedtoproduceaccelerationonlyveryrecentlyintheevolutionoftheuniverse.Anotherpossiblecandidateisdynamicaldarkenergyinwhichthedarkenergyisduetothepotentialenergyofascalarfield,similartothemechanismthatisthoughttodriveinflationintheearlyuniverse[17,18,19,20,21,22,23,24,25,26,27,28].Aconvenientparameterizationofsuchmodelsistheequationofstateparameter,w=p/ρ,thepressuredividedbytheenergydensityofthedarkenergy.Forw∼constant,theSNeIameasurementsandotherobservationsrestrictthisparametertotherange−1.62w−0.74[29],whichprovidesastringentconstraintonseveralinterestingdynamicaldarkenergymodels.Acosmologicalconstantwouldyieldw=−1.Iffutureobservationsindicatew−1,thiswouldimplynewphysicsinthedarksector,eitherarapidlyvaryingw[30],aviolationofagenerallyacceptedconditiononmattercalledthedominantenergycondition[26],oramorecomplicateddarksectornotyetexplored.Moreover,thoughtheCDMmodelwithacosmologicalconstant,knownasΛCDM,impressivelyfitsthecurrentobservations,newmeasurementsinthenearfuturewillputtheΛCDMmodelthroughstricttests.ItwillbeusefultohavemoregeneraldarksectormodelsaroundtobothactasafoiltoΛCDMandasapossiblereplacementshoulditfailfuturetests.Onepossibilityforamorecomplicateddarksectormode