BBN And CMB Constraints On Dark Energy

arXiv:astro-ph/0210500v22Feb2003BBNAndCMBConstraintsOnDarkEnergyJamesP.KnellerDepartmentofPhysics,TheOhioStateUniversity,Columbus,OH43210DepartmentofPhysics,NorthCarolinaStateUniversity,Raleigh,NC27695-8202∗GarySteigmanDepartmentofPhysics,TheOhioStateUniversity,Columbus,OH43210†DepartmentofAstronomy,TheOhioStateUniversity,Columbus,OH43210(Dated:February2,2008)Currentobservationaldatafavorcosmologicalmodelswhichdifferfromthestandardmodelduetothepresenceofsomeformofdarkenergyand,perhaps,byadditionalcontributionstothemorefamiliardarkmatter.PrimordialnucleosynthesisprovidesawindowontheveryearlyevolutionoftheuniverseandconstraintsfromBigBangNucleosynthesis(BBN)canboundtheparametersofmodelsfordarkmatter/energyatredshiftsofordertenbillion.ThespectrumoftemperaturefluctuationsimprintedontheCosmicMicrowaveBackground(CMB)radiationopensacompletelydifferentwindowontheuniverseatepochsfromredshiftsofordertenthousandtonearlythepresent.TheCMBanisotropyspectrumprovidesconstraintsonnewphysicswhichareindependentof,andcomplementarytothosefromBBN.Hereweconsiderthreeclassesofmodelsforthedarkmatter/energy:extraparticleswhichwererelativisticduringtheearlyevolutionoftheuniverse(“X”);Quintessencemodelsinvolvingaminimally-coupledscalarfield(“Q”);modelswithanon-minimallycoupledscalarfieldwhichmodifythestrengthofgravityduringtheearlyevolutionoftheuniverse(“G”).WeconstraintheparametersofthesemodelsusingdatafromBBNandtheCMBandidentifytheallowedregionsintheirparameterspacesconsistentwiththemoredemandingjointBBNandCMBconstraints.For“X”and“Q”suchconsistencyisrelativelyeasytofind;itismoredifficultforthe“G”modelswithaninversepowerlawpotentialforthescalarfield.I.INTRODUCTIONCurrentandongoingspaced-basedandground-basedobservationalprogramshaveprovidedincreasinglypre-cisedataenablingustoviewthepresentandrecentuniversewithhithertounprecedentedclarityanddetail.Thesedatahaveledtoacurrent“standard”modelofcosmologyinwhich“darkmatter”and“darkenergy”ofunknownoriginsplaysignificantroles.Atthesametime,theearlier,radiationdominated(RD)evolutionoftheuniverseremainslargelyhiddenfromview.Theseearlyepochs,whichmayharborvaluablecluestothenatureofthedarkmatter/energyareshroudedbythehugeopticaldepthofthepre-recombinationplasma.Asaresult,theycanonlybeexploredindirectly,throughthecomparisonswithobservationsofthepredictionsofprimordialnucle-osynthesis(“bigbangnucleosynthesis”:BBN)andofthetemperaturefluctuationsinthespectrumofthecosmicmicrowavebackgroundradiation(CMB).StudiesofBBNandtheCMBofferavaluablecomplementtoprobesoftherecentstructureandevolutionoftheuniverseand,inconjunctionwiththem,mayprovideuniqueconstraintsoncompetingmodelsforthedarkenergy.Forexample,althoughtheabundancesofthelightelementsproducedduringBBNdependlargelyontheuniversaldensityofbaryons,theyarealsosensitivetotheearlyuniverseex-pansionratewhich,inturn,isdeterminedbytheenergy∗currentaddress†mailingaddressdensityinrelativisticparticlesand,onthestrengthofgravity.Thus,BBNcannotonlyconstrainthecontribu-tionofadditionalenergydensitybeyondthatpredictedforthestandardmodelofparticlephysics,itcanalsoprobethestrengthofthegravitationalinteractiondur-ingsuchearlyepochs.Similarly,theCMBfluctuationspectrumdependsnotonlyonthetotalenergydensityandthemagnitudeofitsrelativisticcomponent,butalsoontheexpansionrateandthestrengthofgravity.Asaresult,BBNandtheCMBhavethepotentialtodistin-guishamong–oratleastconstrain–competingmodelsforthedarkenergysomeofwhichleavethestrengthofthegravityinvariantwhileaddingtotheenergydensity,whileothersmaymodifyboth.Inthispaperwecompareandcontrastthemodifica-tionstothestandardmodelBBNandCMBpredictionsinthepresenceofextra,relativisticenergy(“equivalentneutrinos”),forthosemodelsof“Quintessence”which,duringRDepochs,contributeafixedfractionoftherel-ativisticenergydensity,andfornon-minimallycoupledscalarfields(oneofwhoseeffectsistoalterthestrengthofthegravitationalconstantG).Afteranintroductionto,andanoverviewofthenon-standardcosmologiesex-ploredhere(§II),theBBNpredictionsforthesethreegeneralmodelsarecomparedandcontrastedandcurrentdataisemployedtoprovideconstraintsonthemin§III.In§IVanoverviewisprovidedofthephysicaloriginoftheCMBfluctuationsinthestandardmodelasapreludetoourdiscussionofthepredictionsinthenon-standardcosmologies(§V).TheCMBconstraintsarepresentedin§VIandin§VIItheyarecombinedwiththosefromBBNtoprovidejointconstraintsonthenon-standardcosmolo-2giesconsideredhere.OurresultsonthejointBBN-CMBconstraintsaresummarizedin§VIII.Unlessotherwisestated,weuseunitsinwhich¯h=c=8πG=1.II.NON-STANDARDCOSMOLOGIESBeforewebegindiscussingtheimplicationsforBBNandtheCMBofthe“newphysics”weareconsideringitisworthspendingsometimeinvestigatingtheeffectsofeachuponcosmologyingeneral.Asareferencewetakethestandardmodeltobegeometricallyflat,containingthree,lightneutrinos,baryonsalongwithcolddarkmat-ter(CDM),andacosmologicalconstant(Λ).Fornu-mericalestimateswewilloftenadopttheso-calledcon-cordancevaluesforthedensityparameters:ΩM=0.3,ΩΛ=1−ΩM=0.7,andforthepresentvalueoftheHubbleparameter:H0=72kms−1Mpc−1.“X”Inmanyextensionsofthestandardmode