Dark matter and dark energy production in quantum

arXiv:astro-ph/0405455v124May2004DarkmatteranddarkenergyproductioninquantummodeloftheuniverseV.E.KuzmichevandV.V.KuzmichevBogolyubovInstituteforTheoreticalPhysics,Nat.Acad.ofSci.ofUkraine,Kiev,03143UkraineAbstractThematter/energystructureofthehomogeneous,isotropic,andspatiallycloseduniverseisstudied.Thequantummodelunderconsiderationpredictsanexistenceoftwotypesofcollectivequantumstatesintheuniverse.Thestatesofonetypecharacterizeagravitationalfield,theothersdescribeamat-ter(uniformscalar)field.Inthefirststageoftheevolutionoftheuniverseaprimordialscalarfieldevolvesslowlyintoitsvacuum-likestate.Fromthepointofviewofsemiclassicaldescriptiontheearlyuniverseisfilledwithprimordialradiationandischargesymmetricinthisstage.Inthesecondstagethescalarfieldoscillatesaboutanequilibriumduetothequantumfluctuations.Theuni-verseisbeingfilledwithmatterintheformofelementaryquantumexcitationsofthevibrationsofthescalarfield.Theseparatequantumexcitationsarecharacterizedbynon-zerovaluesoftheirenergies(masses).Undertheactionofgravitationalforcesmainlytheseexcitationsdecayintoordinaryparticles(baryonsandleptons)anddarkmatter.Theelementaryquantumexcitationsofthevibrationsofthescalarfieldwhichhavenotdecayeduptonowformdarkenergy.ThenumericalestimationsleadtorealisticvaluesofboththematterdensityΩM≃0.29(withthecontributionsfromdarkmatter,ΩDM≃0.25,andopticallybrightbaryons,Ωstars≃0.0025)andthedarkenergydensityΩX≃0.71ifonetakesthatthemeanenergy∼10GeVisreleasedindecayofdarkenergyquantumandfixesbaryoniccomponentΩB=0.04accordingtoobservationaldata.Theenergy(mass)ofdarkenergyquantumisequalto∼17GeVandtheenergy&2×1010GeVisneededinordertodetectit.Darkmatterparticlehasthemass∼6GeV.TheJeansmassfordarkmatterwhichisconsideredasagasofsuchmassiveparticlesisequaltoMJ∼105M⊙.1IntroductionObservationsindicatethatoverwhelmingmajority(about96%)ofmatter/energyintheuniverseisinunknownform(seee.g.Refs.[1,2]forreviews).TheobservedmassofstarsgivesthevalueΩstars≃0.005[3]orevensmallerΩstars≃0.003+0.001−0.00212V.E.KuzmichevandV.V.Kuzmichev[4]forthedensityofvisible(opticallybright)baryons.Observationsofthecosmicmicrowavebackgroundradiation(CMB)andabundancesofthelightelementsintheuniversesuggestthatthetotaldensityofbaryonsisequaltoΩB≃0.04[1,2,5].ThisvalueisoneordergreaterthanΩstars.Itmeansthatmostofbaryonicmattertodayisnotcontainedinstarsandisinvisible(dark).TheCMBanisotropymeasurementsallowtodeterminethetotalenergydensityΩtotandthemattercomponentΩM.Therecentdatagivethestrongevidencethatthepresent-dayuniverseisspatiallyflat(orveryclosetoit)withΩtot≃1[6]andthemeanmatterdensityequalsΩM≃0.3[1].TheindependentinformationaboutΩMextractedfromthehighredshiftsupernovaeIadataontheassumptionthatΩtot=1givestheclosevalues:ΩM=0.28±0.05[7]orΩM=0.29+0.05−0.03[8].ThediscrepanciesbetweenΩMandΩBontheonehandandΩtotandΩMontheotherhandaresignsthattheremustexistnon-baryonicdarkmatterwiththedensityΩDM=ΩM−ΩB∼0.3andsomemysteriouscosmicsubstance(so-calleddarkenergy[9])withthedensityΩX=Ωtot−ΩM∼0.7.Theoriginandcompositionofbothdarkmatteranddarkenergyareunknown.Darkmattermanifestsitselfintheuniversethroughthegravitationalinteraction.Itspresenceallowstoexplainrotationcurvesforgalaxiesandlarge-scalestructureoftheuniverseinthemodelswithstandardassumptionofadiabaticdensityperturbations[1,2,10].Candidatesfordarkmatteranddarkenergyarediscussede.g.inreviews[1,2,10,11].Asregardsdarkenergyitisworthmentioningthatitsexpectedpropertiesareunusual.Itisunobservable(innowaycoulditbedetectedingalaxies)andspatiallyhomogeneous.Thusthepresentdataofmoderncosmologyposetheprinciplequestionaboutthenatureofthemass-energyconstituentsoftheuniverseandtheirpercentageinthetotalenergydensity.Effortsinthisdirectionwerefocusedonachoiceofcandidatesfordarkmatteranddarkenergybetweenknown(realorhypothetical)particlesandfields.ItisobviousthatreasonablecosmologicaltheorymustfirstofallanswerthequestionwhythedensitiesΩMandΩXinthepresenteraarecomparablebetweenthemselves(so-calledcoincidenceproblem)andexplaintheobservedratioΩB/Ωstars∼O(10).InthepresentpapertheproblemofdarkmatteranddarkenergyisstudiedinthecontextofthequantummodeloftheuniverseproposedinRefs.[12,13].ThefirstattemptstogiveananswertothequestionaboutthenatureofdarkmatteranddarkenergyonthebasisofquantumapproachtocosmologicalproblemsweremadeinRefs.[14,15].InSec.2thebasicequationsofthequantummodelofthehomogeneous,isotropicandspatiallycloseduniversearegiven.Itissupposedthattheuniverseisfilledwithprimordialmatterintheformoftheuniformscalarfield.Timeisintroducedasanembeddingvariablewhichdescribesamotionofsomesource.Fromthepointofviewofsemiclassicalapproachthissourcehasaformofradiation.Theevolutionoftheuniversecanbeconventionallydividedintotwostages.Atthefirststage(Sec.3)thescalarfielddeterminesthevacuumenergydensitywhichslowlyevolvesDarkmatteranddarkenergyproduction3intothestatewithminimaldensity(vacuum-likestate).Radiationispresentasaprimordialsourceanduniverseischargesymmetric.InSec.4thesecondstageoftheevolutionoftheuniverseinconsidered.Atthisstagethescalarfieldoscillatesabouttheequilibriumvacuum-likestat