Field theory model giving rise to quintessential i

arXiv:hep-th/0007144v329Dec2000Fieldtheorymodelgivingriseto”quintessentialinflation”withoutthecosmologicalconstantandotherfinetuningproblemsA.B.Kaganovich∗PhysicsDepartment,BenGurionUniversityoftheNegev,BeerSheva84105,IsraelAfieldtheoryisdevelopedbasedontheideathattheeffectiveactionofyetunknownfundamentaltheory,atenergyscalebelowthePlanckmassMphastheformofexpansionintwomeasures:S=Rd4x[ΦL1+√−gL2]wherethenewmeasureΦisdefinedusingtheantisymmetrictensorfieldΦd4x=∂[αAβγδ]dxα∧dxβ∧dxγ∧dxδ.AshiftL1→L1+constdoesnotaffecttheequationsofmotionwhereasasimilarshiftwhenimplementingwithL2causesachangewhichinthestandardGRwouldbeequivalenttothatofthecosmologicalconstant(CC)term.ThenextbasicconjectureisthattheLagrangiandensitiesL1andL2donotdependofAμνλ.Thenewmeasuredegreesoffreedomresultinthescalarfieldχ=Φ/√−galone.Theconstraintappearsthatdeterminesχintermsofmatterfields.Aftertheconformaltransformationtothenewvariables(Einsteinframe),allequationsofmotiontakethecanonicalGRformoftheequationsforgravityandmatterfieldsand,thereforethemodelswestudyarefreeofthewell-known”defects”thatdistinguishtheBrans-DicketypetheoriesfromEinstein’sGR.Allnoveltyisrevealedonlyinanunusualstructureoftheeffectivepotentialsandinteractionswhichturnsoverourintuitiveideasbasedonourexperienceinfieldtheory.Forexample,thegreaterΛweadmitinL2,thesmallermagnitudeoftheeffectiveinflatonpotentialU(φ)willbeintheEinsteinpicture.Fieldtheorymodelsaresuggestedwithexplicitlybrokenglobalcontinuoussymmetry,whichintheEinsteinframehastheformφ→φ+const.Thesymmetryrestorationoccursasφ→∞.AfewmodelsarepresentedwheretheeffectivepotentialU(φ)isproducedwiththefollowingshape:forφ∼−Mp,U(φ)hastheformtypicalforinflationmodel,e.g.U=λφ4withλ∼10−14;forφ∼−Mp,U(φ)hasmainlytheexponentialformU∼e−aφ/Mpwithvariablea:a=14for−Mp∼φ∼Mp,thatgivesthepossibilityfornucleosynthesisandlarge-scalestructureformation;a=2forφ∼Mp,thatimpliesthequintessenceera.ThereisnoneedofanyfinetuningtopreventappearanceoftheCCtermoranyothertermsthatcouldviolatetheflatnessofU(φ)atφ≫Mp.λ∼10−14isobtainedwithoutfinetuningaswell.Quantizedmatterfieldsmodels,includingspontaneouslybrokengaugetheories,canbeincorporatedwithoutalteringthementionedaboveresults.DirectcouplingoffermionstotheinflatonresemblestheWetterich’smodelbutthereisapossibilitytoavoidanyobservableeffectatthelateuniverse.SSBdoesnotraiseanyproblemswiththeCCinthelateuniverse.PACSnumber(s):11.15.Ex,98.80.Cq,12.10.Dm,04.90.+e∗[e-mail]-redshiftandCMBdata[1]suggestthatasmalleffectivecosmologicalconstantgivesadominantcontributiontotheenergydensityofthepresentuniverse.Amongtheattemptstodescribethispicture,theideatoprofitbythepropertiesofaslow-rollingscalarfield(quintessencemodel)[2]-[8]seemstobethemostattractiveandsuccessful.Insuchapproach,thepresentvacuumenergydensityρvac∼10−47(GeV)4hastobeimitatedbytheenergydensityofaslowlyrollingscalarfielddownitspotentialU(φ)whichpresumablyapproacheszeroasφ→∞.Howeverallknownquintessencemodelscontaintwofundamentalproblems:1.Thecosmologicalconstantproblem[9],[10]remainsinthequintessencemodelsaswell:particlephysicsandcosmologymustgiveadistinctmechanismthatenforcestheeffectivecosmologicalconstanttodecayfromanextremelylargevalueintheveryearlyuniversetotheextremelysmallpresentvaluewithoutfinetuningofparametersandinitialconditions.2.AllknownquintessencemodelsarebasedonthechoiceofsomespecificformforthepotentialU(φ).ThegeneralfeatureofthepotentialsneededtorealizequintessenceisthatU(φ)mustbeflatenoughasφislargeenoughinordertoprovideconditionsfortheslow-rollapproximation.Howeveritisnotclearwhathappenswithotherpossibletermsinthepotential,includingquantumcorrections(seeKoldaandLyth,[11]).Infact,thepotentialmayforinstancecontaintermsthatconstituteastructureofpolynomialsinφ(andφnlnφ)andtheyarenotnegligibleasφislarge,unlessanextremefinetuningisassumedforthemassandself-couplings.Forexample,therestrictionoftheflatnessconditionsonthequarticself-interactionλφ4is[11]λ≪10−120(Mpφ)2.InthispaperIamgoingtopresentafieldtheorymodelthatresolvestheabovefinetuningproblemsandbesidesthat,thismodelisabletogiveabroadrangeoftoolsforconstructiveanswersfewmoreimportantquestions:3.IntheframeworkofamodelwherepotentialU(φ)oftheexponentialorinversepowerlow(ortherecombinations[8])formplaystheroleofaquintessentialpotentialasφislargeenough,thequestionariseswhatisthecosmologicalroleofsuchU(φ)asφisclosetozeroornegative.Ifsomeotherscalarfieldisresponsibleforaninflationoftheearlyuniverse,thenafieldtheoryhastoexplainwhythepotentialU(φ)ofthescalarfieldφisnegligibleasφisclosetozeroornegative.However,ifthesamequintessencefieldφplaysalsotheroleoftheinflaton[12],[13](intheearlyuniverse)thenagainafieldtheoryhastoexplain[14]anoriginoftherelevanteffectivepotential.Ofcoursethisisanontrivialproblem.Forexample,PeeblesandVilenkin[13]havepresentedaninterestingmodelofasinglescalarfieldthatdrivestheinflationoftheearlyuniverseandendsupasquintessence.TheyadoptthemonotonicpotentialU(φ)=λm41+(φ/m)4forφ0,=λm41+(φ/m)αforφ≥0(1)whereα=const0(forexample4or6)andtheparametersλ=10−14andm=8×105GeVwereadjusted