Cosmology with High-redshift Galaxy Survey Neutrin

arXiv:astro-ph/0512374v35Jun2006CosmologywithHigh-redshiftGalaxySurvey:NeutrinoMassandInflationMasahiroTakada1,EiichiroKomatsu2andToshifumiFutamase11AstronomicalInstitute,TohokuUniversity,Sendai980-8578,Japanand2DepartmentofAstronomy,TheUniversityofTexasatAustin,Austin,TX78712High-zgalaxyredshiftsurveysopenupexcitingpossibilitiesforprecisiondeterminationsofneu-trinomassesandinflationarymodels.Thehigh-zsurveysaremoreusefulforcosmologythanlow-zonesowingtomuchweakernon-linearitiesinmatterclustering,redshift-spacedistortionandgalaxybias,whichallowsustousethegalaxypowerspectrumdowntothesmallerspatialscalesthatareinaccessiblebylow-zsurveys.Wecanthenutilizethetwo-dimensionalinformationofthelinearpowerspectruminangularandredshiftspacetomeasurethescale-dependentsuppressionofmatterclusteringduetoneutrinofree-streamingaswellastheshapeoftheprimordialpowerspectrum.Toillustratecapabilitiesofhigh-zsurveysforconstrainingneutrinomassesandtheprimordialpowerspectrum,wecomparethreefutureredshiftsurveyscovering300squaredegreesat0.5z2,2z4,and3.5z6.5.Wefindthat,combinedwiththecosmicmicrowavebackgrounddataexpectedfromthePlancksatellite,thesesurveysallowprecisiondeterminationofthetotalneutrinomasswiththeprojectederrorsofσ(mν,tot)=0.059,0.043,and0.025eV,respectively,thusyieldingapositivedetectionoftheneutrinomassratherthananupperlimit,asσ(mν,tot)issmallerthanthelowerlimitstotheneutrinomassesimpliedfromtheneutrinooscillationexperiments,byuptoafactorof4forthehighestredshiftsurvey.Theaccuraciesofconstrainingthetiltandrunningindexoftheprimordialpowerspectrum,σ(ns)=(3.8,3.7,3.0)×10−3andσ(αs)=(5.9,5.7,2.4)×10−3atk0=0.05Mpc−1,respectively,aresmallerthanthecurrentuncertaintiesbymorethananor-derofmagnitude,whichwillallowustodiscriminatebetweencandidateinflationarymodels.Inparticular,theerroronαsfromthefuturehighestredshiftsurveyisnotveryfarawayfromthepredictionofaclassofsimpleinflationarymodelsdrivenbyamassivescalarfieldwithself-coupling,αs=−(0.8−1.2)×10−3.PACSnumbers:95.55.Vj,98.65.Dx,98.80.Cq,98.70.Vc,98.80.EsI.INTRODUCTIONWearelivinginthegoldenageofcosmology.Vari-ousdatasetsfromprecisionmeasurementsoftempera-tureandpolarizationanisotropyinthecosmicmicrowavebackground(CMB)radiationaswellasthoseofmatterdensityfluctuationsinthelarge-scalestructureoftheuniversemappedbygalaxyredshiftsurveys,Lyman-αforestsandweakgravitationallensingobservationsareinaspectacularagreementwiththeconcordanceΛCDMmodel[1,2,3,4].Theseresultsassurethattheoryofcos-mologicallinearperturbationsisbasicallycorrect,andcanaccuratelydescribetheevolutionofphotons,neu-trinos,baryons,andcollisionlessdarkmatterparticles[5,6,7],forgiveninitialperturbationsgeneratedduringinflation[8,9].Thepredictionsfromlinearperturbationtheorycanbecomparedwiththeprecisioncosmologicalmeasurements,inordertoderivestringentconstraintsonthevariousbasiccosmologicalparameters.Futureobser-vationswithbettersensitivityandhigherprecisionwillcontinuetofurtherimproveourunderstandingoftheuni-verse.Fluctuationsindifferentcosmicfluids(darkmatter,photons,baryons,andneutrinos)imprintcharacteristicfeaturesintheirpowerspectra,owingtotheirinterac-tionproperties,thermalhistory,equationofstate,andspeedofsound.Aremarkableexampleistheacousticoscillationinthephoton-baryonfluidthatwasgeneratedbeforethedecouplingepochofphotons,z≃1088,whichhasbeenobservedinthepowerspectrumofCMBtem-peratureanisotropy[10],temperature–polarizationcrosscorrelation[11],anddistributionofgalaxies[12,13].Yet,thelatestobservationshaveshownconvincinglythatwestilldonotunderstandmuchoftheuniverse.Thestandardmodelofcosmologytellsusthattheuniversehasbeendominatedbyfourcomponents.Inchronolog-icalorderthefourcomponentsare:earlydarkenergy(alsoknownas“inflaton”fields),radiation,darkmat-ter,andlate-timedarkenergy.Thestrikingfactisthatwedonotunderstandtheprecisenatureofthree(darkmatter,andearlyandlate-timedarkenergy)outofthefourcomponents;thus,understandingthenatureofthesethreedarkcomponentshasbeenandwillcontinuetobeoneofthemostimportanttopicsincosmologyinnextdecades.Ofwhich,onemightbehopefulthatthenextgenerationparticleacceleratorssuchastheLargeHadronCollider(comingon-linein2007)wouldfindsomehintsforthenatureofdarkmatterparticles.Ontheotherhand,thenatureoflate-timedarkenergy,whichwasdis-coveredbymeasurementsofluminositydistanceouttodistantTypeIasupernovae[14,15],isacompletemys-tery,andmanypeoplehavebeentryingtofindawaytoconstrainpropertiesofdarkenergy(see,e.g.,[16]forareview).Howabouttheearlydarkenergy,inflatonfields,whichcausedtheexpansionoftheuniversetoaccelerateintheveryearlyuniverse?Weknowlittleaboutthenatureofinflaton,justlikeweknowlittleaboutthenatureoflate-timedarkenergy.Therequiredpropertyofinfla-tonfieldsisbasicallythesameasthatofthelate-time2darkenergycomponent:bothmusthavealargenegativepressurewhichislessthan−1/3oftheirenergydensity.Toproceedfurther,however,oneneedsmoreinformationfromobservations.Differentinflationmodelsmakespe-cificpredictionsfortheshapeofthepowerspectrum[8](seealsoAppendixB)aswellasforotherstatisticalprop-erties[17]ofprimordialperturbations.Therefor