Dynamics of interacting phantom scalar field dark

arXiv:0808.1382v2[gr-qc]3Sep2008DynamicsofinteractingphantomscalarfielddarkenergyinLoopQuantumCosmologyXiangyunFu1,2,HongweiYu1,2,∗andPuxunWu31DepartmentofPhysicsandInstituteofPhysics,HunanNormalUniversity,Changsha,Hunan410081,China2KeyLaboratoryofLowDimensionalQuantumStructuresandQuantumControlofMinistryofEducation,HunanNormalUniversity,Changsha,Hunan410081,P.R.China3DepartmentofPhysicsandTsinghuaCenterforAstrophysics,TsinghuaUniversity,Beijing100084,ChinaAbstractWestudythedynamicsofaphantomscalarfielddarkenergyinteractingwithdarkmatterinloopquantumcosmology(LQC).Twokindsofcouplingoftheformαρm˙φ(caseI)and3βH(ρφ+ρm)(caseII)betweenthephantomenergyanddarkmatterareexaminedwiththepotentialforthephantomfieldtakentobeexponential.Forbothkindsofinteractions,wefindthatthefuturesingularityappearinginthestandardFRWcosmologycanbeavoidedbyloopquantumgravityeffects.IncaseII,ifthephantomfieldisinitiallyrollingdownthepotential,theloopquantumeffecthasnoinfluenceonthecosmiclatetimeevolutionandtheuniversewillaccelerateforeverwithaconstantenergyratiobetweenthedarkenergyanddarkmatter.PACSnumbers:95.36.+x,04.60.Pp,98.80.-k∗Correspondingauthor1I.INTRODUCTIONRecently,presentacceleratingexpansionofouruniversehasbeenconfirmedbymanyobservations,suchasthecosmicmicrowavebackground(CMB)anisotropy,typeIasuper-novae,andlargescalegalaxysurveys[1,2].Inordertoexplainthisobservedphenomena,darkenergyisassumedtoexistintheuniversewithintheframeworkofgeneralrelativ-ity.Darkenergyisanexoticenergycomponentwithnegativepressureandaccountsforabout72%ofpresenttotalcosmicenergy.Inaddition,observationsalsoshowthatthereisanotherdarkcomponentintheuniverse,i.e.,darkmatter,accountingforabout25%oftotalcosmicenergytoday.Thesimplestcandidateofdarkenergyisthecosmologicalconstant.Itis,however,plaguedwiththeso-calledcoincidenceproblemandthecosmo-logicalconstantproblem[3].Thussomedynamicalscalarfields,suchasquintessence[4],phantom[5],quintom[6]andhessence[7],areproposedaspossiblecandidatesofdarkenergy.Itisworthytonote,however,thatforthesescalarfieldmodelsthecoincidenceproblemstillremains.Althoughthetwodarkcomponentsareusuallystudiedundertheassumptionthatthereisnointeractionbetweenthem,onecannotexcludesuchapossibility.Infact,researchesshowthatapresumedinteractionmayhelpalleviatethecoincidenceproblem[8].Thereforeinteractingdarkenergymodelshaveattractedagreatdealofinterest.MostofthepresentstudiesondarkenergyarecarriedoutintheframeworkofclassicalEinsteingravity.However,itiscommonlybelievedthatquantumgravityeffectswouldplayaroleintheevolutionoftheuniverse.Therefore,itisdesirabletoexaminethepropertiesofdarkenergyinatheoryofquantumgravity.OneofsuchtheorieswhichweareinterestedinthepresentpaperisLoopQuantumGravity(LQG)(seee.g.[9,10,11,12]forreviews),whichisanonperturbativebackgroundindependenttheory.Atthequantumlevel,theclassicalspacetimecontinuumisreplacedbyadiscretequantumgeometryandtheoperatorscorrespondingtogeometricalquantitieshavediscreteeigenvalues.LQGhasbeenappliedincosmologicalcontextasseeninvariousliteraturewhereitisknownasLoopQuantumCosmology(LQC)[13,14,15,16].TheeffectsofloopquantumgravitymodifythestandardFriedmannequationbyaddingintoitacorrectionterm−ρ2/ρcwhich2essentiallyencodesthediscretequantumgeometricnatureofspacetime[16,17,18].LetusnotethatalthoughextratermssuchasthosederivedinRef.[19]areinprinciplepossible,theeffectofsuchtermsisnegligibleforallpracticalpurposes[20].Whenthiscorrectiontermbecomesdominant,theuniversebeginstobounceandthenoscillatesforever.Thereforeboththefuturesingularityandthesingularityatsemi-classicalregimecanbeavoided[16,18,21,22,23].Recently,thedynamicsofphantom,quintomandhessenceinloopquantumcosmologyhavebeenstudied[23,24,25]andbehaviorsdifferentfromthatinthestandardFRWcosmology,suchtheavoidanceoffuturesingularities,arefound.Atthispoint,itshouldalsobenotedherethattheLQCmodification,althoughveryinteresting,isonlyderivedforpureisotropyandisnotveryclearhowitfitswithinbroadermodels.Inthispaper,wewilldiscussthedynamicsofaphantomscalarfielddarkenergy,coupledtodarkmatterinloopquantumcosmology,toseeinwhatwaytheLQGeffectswouldaffectthecosmologicalevolutionofthesystem.Twokindsofinteractionsoftheform,αρm˙φ[26]and3βH(ρφ+ρm)[8],willbestudied.ItisworthpointingoutthatthefirstcouplingcouldariseinstringtheoryorafteraconformaltransformationofBrans-Dicketheory,whilethesecondismotivatedbyanalogywithdissipationofcosmologicalfluidsandhasbeenproposedforapossibledynamicalsolutiontothecoincidenceproblem.Letusnoteherethatthephantomfield,althoughaviablecandidateofdarkenergy,alsohassomestrangeproperties,suchasbeingunstabletovacuumdecayandtheviolationofthedominantenergycondition.II.LOOPQUANTUMCOSMOLOGYByincorporatingtheeffectsofloopquantumgravitywhichessentiallyencodethedis-cretequantumgeometricnatureofspacetime,theeffectivemodifiedFriedmannequation3inaflatuniverseisgivenby[16,17,18,21,27]1H2=ρ31−ρρc,(1)whereH≡˙a/aistheHubbleparameter,ρisthetotalenergydensity,andadotdenotesthederivativewithrespecttocosmictimet.Hereweset8πG≡1;andthecriticalloopquantumdensityisρc≡√316π2γ3G2~,(2)whereγisthed