Weak Lensing and Dark Energy

arXiv:astro-ph/0106399v229Oct2001WeakLensingandDarkEnergyDraganHutererDepartmentofPhysicsEnricoFermiInstituteTheUniversityofChicagoChicago,IL60637-1433Westudythepowerofupcomingweaklensingsurveystoprobedarkenergy.Darkenergymod-ifiesthedistance-redshiftrelationaswellasthematterpowerspectrum,bothofwhichaffecttheweaklensingconvergencepowerspectrum.Somedark-energymodelspredictadditionalclusteringonverylargescales,butthisprobablycannotbedetectedbyweaklensingaloneduetocosmicvariance.Withreasonablepriorinformationonothercosmologicalparameters,wefindthatasurveycovering1000sq.deg.downtoalimitingmagnitudeofR=27canimposeconstraintscomparabletothoseexpectedfromupcomingtypeIasupernovaandnumber-countsurveys.Thisresult,however,iscontingentonthecontrolofbothobservationalandtheoreticalsystematics.Concentratingonthelatter,wefindthatthenonlinearpowerspectrumofmatterperturbationsandtheredshiftdistributionofsourcegalaxiesbothneedtobedeterminedaccu-ratelyinorderforweaklensingtoachieveitsfullpotential.Finally,wediscussthesensitivityofthethree-pointstatisticstodarkenergy.I.INTRODUCTIONRecentdirectevidenceforaccelerationoftheuniverse[1,2]hasspurredconsiderableactivityinfindingwaystoprobethesourceofthisacceleration,darkenergy[3,4,5,6](forareviewofdarkenergyseeRef.[7]).Be-causedarkenergyvarieswithredshiftmoreslowlythanmatter,itstartscontributingsignificantlytotheexpan-sionoftheuniverseonlyrelativelyrecently,atz∼2.Thiscomponentisbelievedtobesmooth(ornearlyso),andthereforedetectablemainlythroughitseffectontheexpansionrateoftheuniverse.Forthesereasons,itisgenerallybelievedthattypeIasupernovae(SNeIa)andnumber-countsurveysofgalaxiesandgalaxyclus-tershavethemostleveragetoprobedarkenergy,astheyprobethedistanceandvolumeinthedesiredred-shiftrange[8].Indeed,plannedsupernovasurveys(e.g.,SNAP[†])andnumber-countmethods[9,10]areex-pectedtoimposetightconstraintsonthesmoothcom-ponent;forexample,σ(w)≈0.05fromSNAP,assumingaflatuniverse.Theprogramofweakgravitationallensing(WL)ispri-marilyorientedtowardmappingthedistributionofmat-terintheuniverse.Thepathsofphotonsemittedbydistantobjectsandtravellingtowardusareperturbedduetotheinterveningmass.Theweaklensingregimecorrespondstotheinterveningsurfacedensityofmatterbeingmuchsmallerthansomecriticalvalue;inthatcasetheobservedobjects(e.g.galaxies)areslightlydistorted.Theweaklensingdistortionsaresmall(roughlyatthe1%[†])andoneneedsalargesampleofforegroundgalaxiesinordertoseparatethelensingeffectfromthe“noise”representedbyrandomorientationsofgalaxies.There-fore,observationsoflensedgalaxiesprovidesinformationonthematterdistributionintheuniverse,aswellasthegrowthofdensityperturbations.AlthoughthepotentialofWLhasbeenrecognizedforaroundtwodecades(e.g.[11]),onlyinthe1990swasthereasurgeofinterestinthisarea[12,13,14,15,16,17]AuniquepropertyofWListhatitissensitivedirectlytotheamountofmassintheuniverse,avoidingthethornyissueofgalaxy-to-massbias.Bymeasuringellipticitiesofalargenumberofgalaxies,onecaninprincipledirectlyreconstructthemassdensityfieldofaninterveningmassiveobject[18].Indeed,themassreconstructionofgalaxyclustershasbeensuccessfullyperformedonanumberofclusters(forareview,seeRef.[19]).Anexcitingrecentdevelopment,relevanttothiswork,wasthediscoveryofweaklensingbylarge-scalestruc-ture,announcedbyfourgroups[20,21,22,23].Theresultsareinmutualagreementandconsistentwiththe-oreticalexpectations,whichisremarkablegiventhattheywereobtainedindependently.Althoughcurrentdataim-poseweakconstraintsoncosmology(e.g.,ruleouttheEinstein-deSitterUniversewithΩM=1),futuresurveyswithlargerskycoverageandimprovedsystematicsareexpectedtoimposeinterestingconstraintsoncosmolog-icalparameters.Thegoalofthisworkistoassessthepowerofweaklensingtoconstraindarkenergy.ThisanalysisthereforecomplementsthatofHuterer&Turner[8],wheretheefficacyofSNeIaandnumber-countsurveyswascon-sidered.Wefollowthestandardpracticeofconsideringdarkenergytobeasmoothcomponentparameterizedbyitsenergydensity(scaledtocritical)ΩXandequation-2of-stateratiow=p/ρ[24].DarkenergymodifiestheWLobservablesbyalteringthedistance-redshiftrelationandthegrowthofdensityperturbations.AsdiscussedinSec.VIB,thenonlinearevolutionofperturbationsalsodependsondarkenergy;thisdependenceismuchmoredifficulttocalculateandneedstobecalibratedfromN-bodysimulations.Overall,thedependenceofWLondarkenergyissomewhatindirectandexpectedtobeweak,especiallywhendegeneracywithothercosmolog-icalparametersistakenintoaccount.Nevertheless,weshallshowthat,providedsystematicerrorsarecontrolledandtheoreticalpredictionssharpened,WLsurveyscanbeefficientprobesofdarkenergy,comparabletoSNeIaandnumber-counts.Proposeddeepwide-fieldsur-veyssuchasLSST[†],theaforementionedSNAP,andVISTA[‡]willattempttoconstraindarkenergythroughtheirWLprograms,makingouranalysisparticularlytimely.PreviousworkonparameterdeterminationfromWLcenteredmostlyonΩMandσ8,thermsdensityfluc-tuationinspheresof8h−1Mpc[16,25];hereH0=100hkm/s/MpcistheHubbleparametertoday.HuandTegmark[26],however,usedtheFishermatrixformal-ismtoaccountforall8parametersuponwhichWLde-pend