Weak lensing in scalar-tensor theories of gravity

1、arXiv:astro-ph/0412120v16Dec2004Weaklensinginscalar-tensortheoriesofgravityCarloSchimd∗Institutd’AstrophysiquedeParis,GRεCO,98bisbdArago,75014Paris(France),andDipartimentodiFisica,Universit`adiParmaINFN-GruppoCollegatodiParmaParcoAreadelleScienze,7/A-43100Parma(Italy)Jean-PhilippeUzan†LaboratoiredePhysiqueTh´eorique,CNRS-UMR8627,Bˆat210,Universit´eParisXI,91415Orsaycedex(France)andInstitutd’AstrophysiquedeParis,GRεCO,98bisbdArago,75014Paris(France).AlainRiazuelo‡Institutd’AstrophysiquedeParis,9。

2、8bisbdArago,75014Paris(France).(Dated:December6,2004)Thisarticleinvestigatesthesignaturesofvariousmodelsofdarkenergyonweakgravitationallens-ing,includingthecomplementarityofthelinearandnon-linearregimes.Itinvestigatesquintessencemodelsandtheirextensiontoscalar-tensorgravity.Thevariouseﬀectsinducedbythissimplestextensionofgeneralrelativityarediscussed.Itisshownthat,giventheconstraintsintheSolarSystem,modelssuchasaquadraticnonminimalcouplingdonotleaveanysignaturesthatcanbedetectedwhileothermodels,。

3、suchasarunawaydilaton,whichincludeattractiontowardgeneralrelativitycanletanimprintofabout10%.PACSnumbers:98.80.Cq,98.80.Es,04.80.CcI.INTRODUCTIONThegrowingevidencesfortheaccelerationoftheuni-versehaveledtotheformulationofnumerousscenariosofdarkenergy(seeRef.[1]forreviews).Inthiscon-structionvariousrouteshavebeeninvestigated[2].Theyreducemainlytotheintroductionofnewdegreesoffree-dominthecosmologicalscenario,eitherasmatterﬁeldswithnegativepressureorinthegravitationalsector.Thesimplestmodelsaccount。

4、ingforthisaccelerationrelyontheintroductionofaslowrollingscalarﬁeldwhoseexpectationvaluevariesduringthehistoryoftheuniverse.Thesequintessencemodels[3]arecharacterizedbytheirpotentialandnumerouschoiceshavebeendis-cussedintheliterature[1].Genericallythisscalarﬁeldmayalsocoupletomatterﬁelds[4].Asaconsequence,thevaluesofthefundamentalconstantswilldependonthevalueofthisﬁeldandmayvary[5]anditwillinduceaﬁfthforcethatwillbelongrangeifthescalarﬁeldislight,whichisusuallythecaseifitisthesourceoftheaccelera。

5、tionoftheuniverse.Inthesimplestextensionofthequintessencemod-∗Electronicaddress:schimd@iap.fr†Electronicaddress:uzan@iap.fr‡Electronicaddress:riazuelo@iap.frels,thequintessenceﬁelduniversallycouplestotheotherﬁelds.Itwasrealizedthatthepropertiesofthisquintessenceﬁeldwereconservedinthatsitua-tion[6,7,8].Thisimpliesthatwearedealingwithascalar-tensortheoryofgravityinwhichthespin-0partnerofthegravitonisalsothequintessenceﬁeld.Fromaphe-nomenologicalpointofview,extendedquintessencemod-elsarethesimplest。

6、welldeﬁnedtheoriesinwhichthereisamodiﬁcationofgravity.Variousobservationalsigna-turesonthebackgroundevolution,thecosmicmicrowavebackground(CMB)anisotropies[8,9,10,11,12],thebig-bangnucleosynthesishavebeenworkedout[13]andthereconstructionproblemwasdiscussedindetails[14].Inparticular,itwasshownthattheattractionmecha-nismtowardgeneralrelativity[15]stillhold[16]intheseextendedquintessencemodels,acrucialpointsincetheyhavetosatisfysharpconstraintsintheSolarSystem[17].Itwasalsopointedoutthatarunawaydil。

7、aton[18,19]thatdoesnotcoupleuniversally,isanappealingmodelswithspeciﬁcsignaturesuchasavariationofsomefun-damentalconstantsandaviolationoftheuniversalityoffreefall.Scalar-tensortheoriesarethemostnaturalalternativetogeneralrelativity[17,20],preservingtheuniversalityoffreefallandconstancyofallnongravitationalcon-stants.Gravityismediatednotonlybyamasslessspin-2graviton,correspondingtothespacetimemetric,butalsobyaspin-0scalarﬁeld.Manytheoreticalmotivationsto2considersuchascalarpartnertothegravitonhav。

8、ebeenputforward,particularlyinhigher-dimensionaltheories.Instringtheory,thesupermultipletofthegravitoncon-tainsadilatonandmoduliﬁelds[21].Scalar-tensortheoriesarewellconstrainedintheSolarsystemandonecantrytoextendtheseconstraintstoastrophysicalandcosmologicalscales.Inthecaseofex-tendedquintessence,theeﬀectofthescalarﬁeldisimpor-tantparticularlyintherecentuniversewhenitstartstodominate.Itwaspointedout[22]thatthemodiﬁcationoftheequationofstateintherecentuniversehasstrik-ingeﬀectsonthegrowthofdensi。

9、typerturbationandonweaklensingobservablessuchastheconvergencepowerspectrum.Weakgravitationallensinghasnowproventobeapowerfultooltostudylargescalestructures[23,24,25]andtogatherinformationonthenatureofthedarkenergy[26,27].Inparticular,cross-correlationtech-niquesseemaverypromisingwaytoachievethistask(seee.g.[28]).Weaklensingcanbedetectedbythede-formationoftheshapeofbackgroundgalaxies.Itwasrecentlyobservedbyvariousgroups[29]andcanprobethelargescalestructuresoftheuniversebothinthelin-earandnon-line。

10、arregimes.Recently,theweaklensinghasbeenstudiedinthecontextofgeneralizedcosmolo-gies[30],specializingtoquadraticnon-minimallycou-pledmodelsandfocusingontheeﬀectsontheCMBanisotropies,hencejustlookingafterthelinearregimeofstructureformation.However,aswasshownonvari-ousexamples[22,26,31],themoststringentconstraintsoncosmologicalmodels,abletodistinguishdarkenergymodels,arisefromthecomparisonofthelinearandnon-linearregimes.Inthisarticle,ourmaingoalistostudyindetailsthelensingobservable,focusingon2-poi。