Weak lensing in scalar-tensor theories of gravity

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,98bisbdArago,75014Paris(France).(Dated:December6,2004)Thisarticleinvestigatesthesignaturesofvariousmodelsofdarkenergyonweakgravitationallens-ing,includingthecomplementarityofthelinearandnon-linearregimes.Itinvestigatesquintessencemodelsandtheirextensiontoscalar-tensorgravity.Thevariouseffectsinducedbythissimplestextensionofgeneralrelativityarediscussed.Itisshownthat,giventheconstraintsintheSolarSystem,modelssuchasaquadraticnonminimalcouplingdonotleaveanysignaturesthatcanbedetectedwhileothermodels,suchasarunawaydilaton,whichincludeattractiontowardgeneralrelativitycanletanimprintofabout10%.PACSnumbers:98.80.Cq,98.80.Es,04.80.CcI.INTRODUCTIONThegrowingevidencesfortheaccelerationoftheuni-versehaveledtotheformulationofnumerousscenariosofdarkenergy(seeRef.[1]forreviews).Inthiscon-structionvariousrouteshavebeeninvestigated[2].Theyreducemainlytotheintroductionofnewdegreesoffree-dominthecosmologicalscenario,eitherasmatterfieldswithnegativepressureorinthegravitationalsector.Thesimplestmodelsaccountingforthisaccelerationrelyontheintroductionofaslowrollingscalarfieldwhoseexpectationvaluevariesduringthehistoryoftheuniverse.Thesequintessencemodels[3]arecharacterizedbytheirpotentialandnumerouschoiceshavebeendis-cussedintheliterature[1].Genericallythisscalarfieldmayalsocoupletomatterfields[4].Asaconsequence,thevaluesofthefundamentalconstantswilldependonthevalueofthisfieldandmayvary[5]anditwillinduceafifthforcethatwillbelongrangeifthescalarfieldislight,whichisusuallythecaseifitisthesourceoftheaccelerationoftheuniverse.Inthesimplestextensionofthequintessencemod-∗Electronicaddress:[e-mail]†Electronicaddress:[e-mail]‡Electronicaddress:[e-mail],thequintessencefielduniversallycouplestotheotherfields.Itwasrealizedthatthepropertiesofthisquintessencefieldwereconservedinthatsitua-tion[6,7,8].Thisimpliesthatwearedealingwithascalar-tensortheoryofgravityinwhichthespin-0partnerofthegravitonisalsothequintessencefield.Fromaphe-nomenologicalpointofview,extendedquintessencemod-elsarethesimplestwelldefinedtheoriesinwhichthereisamodificationofgravity.Variousobservationalsigna-turesonthebackgroundevolution,thecosmicmicrowavebackground(CMB)anisotropies[8,9,10,11,12],thebig-bangnucleosynthesishavebeenworkedout[13]andthereconstructionproblemwasdiscussedindetails[14].Inparticular,itwasshownthattheattractionmecha-nismtowardgeneralrelativity[15]stillhold[16]intheseextendedquintessencemodels,acrucialpointsincetheyhavetosatisfysharpconstraintsintheSolarSystem[17].Itwasalsopointedoutthatarunawaydilaton[18,19]thatdoesnotcoupleuniversally,isanappealingmodelswithspecificsignaturesuchasavariationofsomefun-damentalconstantsandaviolationoftheuniversalityoffreefall.Scalar-tensortheoriesarethemostnaturalalternativetogeneralrelativity[17,20],preservingtheuniversalityoffreefallandconstancyofallnongravitationalcon-stants.Gravityismediatednotonlybyamasslessspin-2graviton,correspondingtothespacetimemetric,butalsobyaspin-0scalarfield.Manytheoreticalmotivationsto2considersuchascalarpartnertothegravitonhavebeenputforward,particularlyinhigher-dimensionaltheories.Instringtheory,thesupermultipletofthegravitoncon-tainsadilatonandmodulifields[21].Scalar-tensortheoriesarewellconstrainedintheSolarsystemandonecantrytoextendtheseconstraintstoastrophysicalandcosmologicalscales.Inthecaseofex-tendedquintessence,theeffectofthescalarfieldisimpor-tantparticularlyintherecentuniversewhenitstartstodominate.Itwaspointedout[22]thatthemodificationoftheequationofstateintherecentuniversehasstrik-ingeffectsonthegrowthofdensityperturbationandonweaklensingobservablessuchastheconvergencepowerspectrum.Weakgravitationallensinghasnowproventobeapowerfultooltostudylargescalestructures[23,24,25]andtogatherinformationonthenatureofthedarkenergy[26,27].Inparticular,cross-correlationtech-niquesseemaverypromisingwaytoachievethistask(seee.g.[28]).Weaklensingcanbedetectedbythede-formationoftheshapeofbackgroundgalaxies.Itwasrecentlyobservedbyvariousgroups[29]andcanprobethelargescalestructuresoftheuniversebothinthelin-earandnon-linearregimes.Recently,theweaklensinghasbeenstudiedinthecontextofgeneralizedcosmolo-gies[30],specializingtoquadraticnon-minimallycou-pledmodelsandfocusingontheeffectsontheCMBanisotropies,hencejustlookingafterthelinearregimeofstructureformation.However,aswasshownonvari-ousexamples[22,26,31],themoststringentconstraintsoncosmologicalmodels,abletodistinguishdarkenergymodels,arisefromthecomparisonofthelinearandnon-linearregimes.Inthisarticle,ourmaingoalistostudyindetailsthelensingobservable,focusingon2-poi