Missing Mass, Dark Energy and the Acceleration of

arXiv:astro-ph/0410710v128Oct2004MissingMass,DarkEnergyandtheAccelerationoftheUniverse.IsAccelerationHeretoStay?Sel¸cukS¸.BayınM[e-mail](February2,2008)TypesetusingREVTEX1AbstractRecentmeasurementsofthetemperaturefluctuationsinthecosmicmicrowaveback-groundradiationindicatethatweliveinanopenuniverse.Sizeofthesefluctuationsalsoindicatethattheuniverseisalmostflat.IntermsFriedmannmodelsthisimpliesamassden-sitywithin10%ofthecriticaldensity.However,thedynamicalmassmeasurementscanonlyaccountforaround30%ofthismass.Recently,aseriesofoutstandingobservationsrevealedthatthecosmosisaccelerating.Thismotivatedsomeastronomerstoexplainthemissing70%assomeexoticdarkenergycalledthequintessenceorasthecosmologicalconstant.InthispaperwepresentanalternativeexplanationtothesecosmologicalissuesintermsoftheFriedmannThermodynamics.Thismodelhasthecapabilityofmakingdefinitepredictionsin-linewiththecurrentobservationsoftheuniverse.Accordingtothismodel,cosmoswasexpandingsloweratthebeginning.Duringthegalaxyformationera;zc∈[0.54,0.91],duetoachangeintheglobalequationofstate,itacceleratesforabriefperiodoftime.WeexpecttoseethisasadiscontinuityintheHubblediagram.Recentdataaboutthegalaxieswithredshifts0.5z0.9displaysthisdiscontinuityclearly.Weexpectthedecelerationtore-appearasmoredatawithredshiftsz&1isgathered.Thesegalaxieswillbeamongtheveryfirstgalaxiesformedintheuniverse,thusstillshowingthekinematicsofthepre-galaxyformationera.ThispointisnowclearlyevidencedintherecentdatabyRiessetal.onTypeIasupernovaewithredshiftsz1.25(2004astro-ph/0402512).Inourmodel,galaxieswithredshifts0.z.0.5shouldreflectthekinematicsoftheuniverseafterthetransitioniscompleted.Thesegalaxiesarenowrecedingfromeachotherfaster.However,forzvaluestowardstheupperendofthisrangewestillexpecttoseedeceleration.Thisisincontrastwiththepredictionsofthedarkenergymodels.2I.INTRODUCTIONOneofthefirstapplicationsoftheEinstein’stheoryofgravitationwasgivenbyEinsteintocosmology.Whichlaterdevelopedintowhatisnowknownasthestandardmodel,andhasbeenextremelysuccessfulinexplainingtheoverallfeaturesoftheuniversetotimesasearlyas10−2sec[1−3].Oneofthebasicfeaturesofthestandardmodel(alsocalledtheFriedmannmodels)isthelargescalehomogeneityandisotropyoftheuniverse.ThisisevidencedintheuniformityofthetemperaturedistributionoftheCMBR(cosmicmicrowavebackgroundradiation).Whichisverifiedtoonepartin105withantennasseparatedbyanglesrangingfrom10arcsecto180degrees.Amongitsothersuccessfulpredictions;wecouldnametheageoftheuniverse,existenceofCMBR,expansionoftheuniverse,abundancesoflightelements,andtheexistenceofstructure.Whenthestandardmodelisextrapolatedtothefirstmicrosecondsoftheuniverse,problemsaboutthehorizonandflatnessappear[1-3].Tosolvetheseproblemsinflationarymodelshavebeenproposed.ToexplainthedetailsoftheuniverseuptothePlancktimeoftheoriginmayindeedbeatallorder,evenforasuccessfultheoryliketheEinstein’stheoryofgravity.However,therearealsoseriousproblemsregardingtherelativelyrecenterasoftheuniverse[1-3].1.MissingMassProblemRecombinationstartswhentheuniversewasabout300,000yearsold.Priortothistime,lightcreatedwiththebigbangwasconstantlybeingscatteredbythefreeelectronsinaplasmaofprimordialhydrogenandheliumatoms.Ataboutthistime,universehassufficientlycooledfortheelectronsandprotonstoformatomshence,scatteringhasstopped.ForthisreasonphotonsthatweseetodayastheCMBRat2.73K,carriesinformationaboutthestateoftheuniversewhenitwasonly300,000yearsold.However,CMBRisnotcompletelyuniform.Thetheorypredictsthatthereshouldexisttemperaturefluctuationsattheorderof10−5inordertoseedstructureformation.Indeed,suchfluctuationshave3beenobservedbyvariousgroups[4-9].Sincecurvatureactslikealens,fromthesizeofthesefluctuationsonecouldobtainvaluableinformationaboutthegeometryoftheuniverse.Comparedtothecriticallyopen(flat)universe,thesefluctuationsshouldappearsmallerforaclosed(spherical),andlargerforanopen(hyperbolic)universe.Mostrecentobservations[4]indicatethatthesizeofthesefluctuationshasnotchangedmuchsincetheywereformed.Thusindicatingthatthegeometryoftheuniverseisveryclosetoflat.Einstein’stheoryrelatesthemattercontentoftheuniversetoitsgeometry.Observationsaboutthegeometryoftheuniverse,consideredwiththeEinstein’sfieldequationsandtheHubbleconstant(H0)measurements,implythatthepresentdensityofmassshouldbewithin10%ofthecriticaldensitydefinedas[4-11]ρc=3H208πG.(1)Thisresultshouldnaturallybeconfirmedbythedynamicalmassmeasurementsintheuniverse.Thisisachallengingtask.Variousmethodsindicatethatonlyaround4%ofthematterisordinarymatteri.e.baryonic.Fromtheorbitalspeedsofgalaxieswithinaclusterwealsoknowthatthereisapproximately6timesasmuchdarkmatterasbaryonicmatter.Darkmatterisbasicallycomposedofparticleslikeneutrinosandotherweaklyinteractingmassiveparticles(WIMPS).Theseparticlesinteractweaklywithothermatteranddonotcluster.However,theirpresencecouldbedetectedthroughtheirgravitationaleffects[4,12-14].Inotherwords,thetotalamountofallkindsofmatter-bothdarkandordinary-intheuniverseonlyaccountsfor30%ofthecriticaldensity.T