Dark energy cosmology from higher-order, string-in

arXiv:hep-th/0605039v324Jul2006Darkenergycosmologyfromhigher-orderstring-inspiredgravityanditsreconstructionShin’ichiNojiri∗DepartmentofPhysics,NagoyaUniversity,Nagoya464-8602.JapanSergeiD.Odintsov†‡Instituci`oCatalanadeRecercaiEstudisAvan¸cats(ICREA)andInstitutdeCienciesdel’Espai(IEEC-CSIC),CampusUAB,FacultatdeCiencies,TorreC5-Par-2apl,E-08193Bellaterra(Barcelona),SpainM.Sami§CentreforTheoreticalPhysics,JamiaMilliaIslamia,NewDelhiandDepartmentofPhysics,JamiaMilliaIslamia,NewDelhi,IndiaInthispaperweinvestigatethecosmologicaleffectsofmodifiedgravitywithstringcurvaturecorrectionsaddedtoEinstein-HilbertactioninthepresenceofadynamicallyevolvingscalarfieldcoupledtoRiemanninvariants.Thescenarioexhibitsseveralfeaturesofcosmologicalinterestforlateuniverse.Itisshownthathigherorderstringycorrectionscanleadtoaclassofdarkenergymodelsconsistentwithrecentobservations.Themodelcangiverisetoquintessencewithoutrecoursetoscalarfieldpotential.Thedetailedtreatmentofreconstructionprogramforgeneralscalar-Gauss-Bonnetgravityispresentedforanygivencosmology.Theexplicitexamplesofreconstructedscalarpotentialsaregivenforaccelerated(quintessence,cosmologicalconstantorphantom)universe.Fi-nally,therelationwithmodifiedF(G)gravityisestablishedonclassicallevelandisextendedtoincludethirdordertermsoncurvature.PACSnumbers:11.25.-w,95.36.+x,98.80.-kI.INTRODUCTIONOneofthemostremarkablediscoveriesofourtimeisrelatedtothelatetimeaccelerationofouruniversewhichissupportedbyobservationsofhighredshifttypeIasupernovaetreatedasstandardizedcandlesand,moreindirectly,byobservationsofthecosmicmicrowavebackgroundandgalaxyclustering.ThecriticalityofuniversesupportedbyCMBobservationsfixesthetotalenergybudgetofuniverse.Thestudyoflargescalestructurerevealsthatnearly30percentofthetotalcosmicbudgetiscontributedbydarkmatter.Thenthereisadeficitofalmost70percent;inthestandardparadigm,themissingcomponentisanexoticformofenergywithlargenegativepressuredubbeddarkenergy[1,2,3,4,5,6,7].Therecentobservationsonbaryonoscillationsprovideyetanotherindependentsupporttodarkenergyhypothesis[8].ThedynamicsofouruniverseisdescribedbytheEinsteinequationsinwhichthecontributionofenergycontentofuniverseisrepresentedbyenergymomentumtensorappearingonRHSoftheseequations.TheLHSrepresentspuregeometrygivenbythecurvatureofspace-time.Gravitationalequationsintheiroriginalformwithenergy-momentumtensorofnormalmattercannotleadtoacceleration.Therearethentwowaystoobtainacceleratedexpansion,eitherbysupplementingenergy-momentumtensorbydarkenergycomponentorbymodifyingthegeometryitself.Darkenergyproblemisoneofthemostimportantproblemsofmoderncosmologyanddespiteofthenumberofefforts(forarecentreview,see[3,4]),thereisnoconsistenttheorywhichmaysuccessfullydescribethelate-timeaccelerationoftheuniverse.GeneralRelativitywithcosmologicalconstantdoesnotsolvetheproblembecausesuchtheoryisinconflictwithradiation/matterdominationeras.Analternativeapproachtodarkenergyisrelatedtomodifiedtheoryofgravity(forareview,see[9])inwhichdarkenergyemergesfromthemodificationofgeometry†alsoatLab.Fundam.Study,TomskStatePedagogicalUniversity,Tomsk∗Electronicaddress:[e-mail],[e-mail]‡Electronicaddress:[e-mail]§Electronicaddress:[e-mail],thereappearsquiteaninterestingpossibilitytomimicdarkenergycosmologybystringtheory.Itwassuggestedinrefs.[10,11,12]thatdarkenergycosmologymayresultfromstring-inspiredgravity.Infact,scalar-Gauss-BonnetgravityfrombosonicorTypeIIstringswasstudiedinthelateuniverse[10,11](forreviewoftheapplicationsofsuchtheoryintheearlyuniverse,see[13]).Itisalsointerestingsuchtheoriesmaysolvetheinitialsingularityproblemofthestandardbig-bangmodel(see[14]andrefs.therein).Moreover,theeasyaccountofnextorder(thirdorder,Lovelockterm)isalsopossibleinthisapproach(forrecentdiscussionofsuchgravity,see[15]).Inthispaperweexaminestring-inspiredgravitywiththirdordercurvaturecorrections(scalar-Gauss-Bonnettermandscalar-Eulerterm)andexplorethecosmologicaldynamicsofthesystemattributingspecialattentiontodarkenergy(non-phantom/phantom)solutions.Weconfrontourresultwiththerecentobservations.Wealsooutlinethegeneralprogramofreconstructionofscalar-Gauss-Bonnetgravityforanyapriorigivencosmologyfollowingthemethod[16]developedinthescalar-tensortheory.Thepaperisorganizedasfollows.Insectiontwo,weconsiderthecosmologicaldynamicsinthepresenceofstringcurvaturecorrectionstoEinstein-Hilbertaction.WeanalyzecosmologicalsolutionsintheFRWbackground;specialattentionispaidatdarkenergywhichnaturallyarisesinthemodelthankstohigherordercurvaturetermsinducedbystringcorrections.Briefdiscussiononthecomparisonoftheoreticalresultswithrecentobservationsisincluded.Thestabilityofdarkenergysolutionisinvestigatedindetail.Sectionthreeisdevotedtothestudyoflate-timecosmologyforscalar-Gauss-Bonnetgravitymotivatedbystringtheorybutwiththearbitraryscalarpotentials.Itisexplicitlyshownhowsuchtheory(actually,itspotentials)maybereconstructedforanygivencosmology.Severalexplicitexamplesofdarkenergycosmologywithtransiti