Cosmological parameter analysis including SDSS Ly-

arXiv:astro-ph/0407372v119Jul2004CosmologicalparameteranalysisincludingSDSSLyαforestandgalaxybias:constraintsontheprimordialspectrumoffluctuations,neutrinomass,anddarkenergyUroˇsSeljak1,AlexeyMakarov1,PatrickMcDonald1,ScottF.Anderson2,NetaA.Bahcall3,J.Brinkmann4,ScottBurles5,RenyueCen3,MamoruDoi6,JamesE.Gunn3,ˇZeljkoIvezi´c3,2,StephenKent7,JonLoveday8,RobertH.Lupton3,JeffreyA.Munn9,RobertC.Nichol10,JeremiahP.Ostriker3,11,DavidJ.Schlegel3,DonaldP.Schneider12,MaxTegmark13,5,DanielE.VandenBerk12,DavidH.Weinberg14,DonaldG.York151PhysicsDepartment,PrincetonUniversity,Princeton,NJ08544,USA;2AstronomyDepartment,UniversityofWashington,Seattle,WA98195,USA3PrincetonUniversityObservatory,Princeton,NJ08544,USA4ApachePointObservatory,2001ApachePointRd,Sunspot,NM88349-0059,USA5Dept.ofPhysics,MassachusettsInstituteofTechnology,Cambridge,MA02139,USA;6InstituteofAstronomy,SchoolofScience,UniversityofTokyo,Japan;7FermiNationalAcceleratorLaboratory,P.O.Box500,Batavia,IL60510,USA;8UniversityofSussex,Sussex,UK;9U.S.NavalObservatory,FlagstaffStation,Flagstaff,AZ86002-1149,USA;10InstituteofCosmologyandGravitation,UniversityofPortsmouth,Portsmouth,UK11InstituteofAstronomy,CambrdigeUniversity,Cambridge,UK12Dept.ofAstronomyandAstrophysics,PennsylvaniaStateUniversity,UniversityPark,PA16802,USA;13DepartmentofPhysics,UniversityofPennsylvania,Philadelphia,PA19104,USA;14DepartmentofAstronomy,OhioStateUniversity,Columbus,OH43210,USA;15DepartmentofAstronomy&Astrophysics,UniversityofChicago,Chicago,IL60637,USA;(Dated:February2,2008.TobesubmittedtoPhys.Rev.D.)WecombinetheconstraintsfromtherecentLy-αforestanalysisoftheSloanDigitalSkySurvey(SDSS)andtheSDSSgalaxybiasanalysiswithpreviousconstraintsfromSDSSgalaxyclustering,thelatestsupernovae,and1styearWMAPcosmicmicrowavebackgroundanisotropies.Wefindsignificantimprovementsonallofthecosmologicalparameterscomparedtopreviousconstraints,whichhighlightstheimportanceofcombiningLyαforestconstraintswithotherprobes.CombiningWMAPandtheLyαforestwefindfortheprimordialslopens=0.98±0.02.Weseenoevidenceofrunning,dn/dlnk=−0.003±0.010,afactorof3improvementoverpreviousconstraints.Wealsofindnoevidenceoftensors,r0.36(95%c.l.).Inflationarymodelspredicttheabsenceofrunningandmanyamongthemsatisfytheseconstraints,particularlynegativecurvaturemodelssuchasthosebasedonspontaneoussymmetrybreaking.Apositivecorrelationbetweentensorsandprimordialslopedisfavorschaoticinflationtypemodelswithsteepslopes:whiletheV∝φ2modeliswithinthe2-sigmacontour,V∝φ4isoutsidethe3-sigmacontour.Fortheamplitudewefindσ8=0.90±0.03fromtheLyαforestandWMAPalone.Wefindnoevidenceofneutrinomass:forthecaseof3massiveneutrinofamilieswithaninflationaryprior,Pmν0.42eVandthemassoflightestneutrinoism10.13eVat95%c.l.Forthe3massless+1massiveneutrinocasewefindmν0.79eVforthemassiveneutrino,excludingat95%c.l.allneutrinomasssolutionscompatiblewiththeLSNDresults.Weexploredarkenergyconstraintsinmodelswithafairlygeneraltimedependenceofdarkenergyequationofstate,findingΩλ=0.72±0.02,w(z=0.3)=−0.98+0.10−0.12,thelatterchangingtow(z=0.3)=−0.92+0.09−0.10iftensorsareallowed.Wefindnoevidenceforvariationoftheequationofstatewithredshift,w(z=1)=−1.03+0.21−0.28.TheseresultsrelyonthecurrentunderstandingoftheLyαforestandotherprobes,whichneedtobeexploredfurtherbothobservationallyandtheoretically,butextensivetestsrevealnoevidenceofinconsistencyamongdifferentdatasetsusedhere.PACSnumbers:PACSnumbers:98.80.EsI.INTRODUCTIONManydifferentcosmologicalobservationsoverthepastdecadehavehelpedbuildwhatisnowcalledthestandardcosmologicalmodel.Theseobservationssuggestthattheuniverseisspatiallyflat,containsbaryons,darkmatteranddarkenergy.Theprimordialspectrumoffluctua-tionsisapproximatelyscaleinvariantandinitialfluctu-ationsareGaussianandadiabatic.Thisstandardcos-mologicalmodelcanbedescribedintermsofonlyafewparameters,whichexplainalargenumberofobserva-tions,suchasthecosmicmicrowavebackground(CMB),galaxyclustering,supernovadata,Hubbleparameterde-terminations,andweaklensing.ThelatestresultscomefromWilkinsonMicrowaveAnisotropyProbe(WMAP)CMBmeasurements[1,2,3],SloanDigitalSkySurvey(SDSS)andTwodegreeField(2dF)galaxyclusteringanalyses[4,5,6],andfromthelatestSupernovaetypeIa(SNIa)data[7,8].Whilethestandardmodelisobservationallywelljus-tified,manytheoreticalmodelspredictthatthereshouldbeobservabledeviationsfromit.Perhapsthebestmo-tivatedamongthesearethepredictionsofhowtheuni-versewasseededbyinitialfluctuations.Thestandardparadigmisinflation,whichpredictsthatthefluctua-tionsshouldbealmost,butnotexactly,scaleinvariant2[9].Atypicaldeviationfortheslopeoftheprimordialperturbationsispredictedtobeoforderofafewpartsinahundredawayfromitsscaleinvariantvaluens=1andcouldbeofeithersign.Thisshouldbeobservablewithhighprecisioncosmologicalobservations.Despitetremendousprogressoverthepastcoupleofyearsthecurrentconstraintsdonotyetdistinguishbetweendif-ferentinflationarymodels[10,11].Alternativemodelsalsopredictdeviationsfromscaleinvariancesimilartoinflation[12].Anotherpredictionofthesemodelsisthattherateofchangeofslopewithscaleisrathersmall,αs=dns/dlnk∼