20. Global cosmological parameters H0, M,andΛ 1 2

20.Globalcosmologicalparameters:H0,ΩM,and120.GLOBALCOSMOLOGICALPARAMETERS:H0,ΩM,andWrittenApril2000byM.Fukugita(UniversityofTokyo,InstituteforCosmicRayResearch)andC.J.Hogan(UniversityofWashington).Thisreviewsurveysthecurrentstatusofthedeterminationofthethreecosmologicalparameters,theHubbleconstantH0,themassdensityparameterΩMandthecosmologicalconstant.Thesequantitiessetthescaleandcharacterizethemeanmass-energycontentandcurvatureincosmologicalsolutionsofEinstein'sequationswhichdescribethegeometryandevolutionoftheuniverseasawhole.Fortechnicaldetails,seeRef.1.WeadoptthenormalizationΩM+Ω=1forzerocurvature(flatuniverse),whereΩ==3H20withbeingthecosmologicalconstantenteringintheEinsteinequation.ThecasewithΩM=1andΩ=0isreferredtoastheEinstein-deSitter(EdS)universe.Weoftenusedistancemodulusm−M=5log(dL=10pc)insteadoftheluminositydistancedL,wheremistheapparentmagnitudeofanobjectwhosemagnitudeat10pcwouldbeM.Weomittheunitkms−1Mpc−1fortheHubbleconstantandadopttheabbreviationh=H0=100.20.1.TheHubbleConstant20.1.1.Overview:TheHubbleconstant,whichhasdimensionofinversetime,setsthescaleofthesizeandageoftheUniverse.Recenteortstomeasureithavealmostsolvedthelong-standingdiscrepancyconcerningtheextragalacticdistancescale;atthesametime,newuncertaintieshavebeenrevealedintheMilkyWaydistancescale.TheglobalvalueofH0wasuncertainbyafactoroftwoforseveraldecades.Before1980thedisputewasbetweentwoschools:SandageandcollaboratorsinsistedonH0=50;deVaucouleursandcollaboratorspreferredahighvalue,H0=90{100.Thedichotomypersistedevenafterthediscoveryofanempiricalbuttightrelationshipbetweenagalaxy'sluminosityandrotationvelocity,knownastheTully-Fisherrelation,whichallowedrelativedistancesbetweenwholegalaxiestobeestimatedfaroutintothesmoothHubbleflow.AstraightforwardreadingoftheTully-FisherrelationgavevaluesH0=80{90,butthisresultwaschallengedovertheissueoftheMalmquistbias|whetherthesampleselectspreferentiallybrightgalaxies,biasingtowardsashorterdistance.ArelateddisputeconcernedthedistancetotheVirgocluster,16Mpcor22Mpc,dependingonthesampleused.Thenextmajoradvancecamein1989{1990whennew,morepreciserelativedistanceindicatorswerediscovered:theapparentlyuniversalshapeofthetheplanetarynebulaluminosityfunction(PNLF),andthesurfacebrightnessfluctuations(SBF)ingalaxyimages,utilizingthefactthatamoredistantgalaxyshowsasmootherlightdistribution.Thetwocompletelyindependentmethodspredictedrelativedistancestoindividualgalaxiesinexcellentagreementwitheachother,andalsowiththeTully-Fisherrelation(albeitwithasomewhatlargerscatter)[2].Thesenewtechniques,whencalibratedwiththedistancetoM31,yieldedavaluearoundH0=80andaVirgodistanceof15Mpc.CITATION:K.Hagiwaraetal.,PhysicalReviewD66,010001-1(2002)availableonthePDG(URL:)June18,200213:57220.Globalcosmologicalparameters:H0,ΩM,andAroundthesametimeTypeIasupernovae(SNeIa)werewidelyadoptedasstandardcandles.ThisledtoH0=50{55,whencalibratedwithaCepheiddistancetothenearestSNIahostgalaxyusingthepre-refurbishedHubbleSpaceTelescope(HST).ThusintheearlyninetiesestimateswerestilldichotomousbetweenH0=50and80.TherefurbishmentofHSTallowedaccuratemeasurementsofCepheidsingalaxiesasdistantas20Mpc.ThissecuredthedistancetotheVirgoclusterandtightenedthecalibrationsoftheextragalacticdistanceindicators,andresultedinH0=(70{75)10,10%lowerthanthe`highvalue'.AnotherimportantcontributionwasthediscoverythatthemaximumbrightnessofSNeIavariesfromsupernovatosupernova,andthatitcorrelatestightlywiththedeclinerateofbrightness.DirectcalibrationofthemaximumbrightnessofseveralSNeIawithHSTCepheidobservationsyieldedH0=65+5−10,andnearlyresolvedthelong-standingcontroversy.AllthemethodsmentionedaboveusedistanceladdersandtakethedistancetotheLargeMagellanicCloud(LMC)tobe50kpc(m−M=18:5)asthezeropoint.Before1997fewdoubtswerecastonthedistancetoLMC.WiththeexceptionofdeterminationsusingRRLyrstars,thedistancemodulusconvergedtom−M=18:50:1,i.e.,witha5%error,andtheRRLyrdiscrepancywasblamedonitslargercalibrationerror.IthadbeenbelievedthattheHipparcosastrometricsatellitewouldsecurethedistancewithintheMilkyWayandtightenthedistancetoLMC.Toeveryone'ssurprise,Hipparcosinsteadrevealedthecontrary:thedistancetoLMCwasmoreuncertainthanwehadthought,introducingnewuncertaintiesintothedeterminationofH0.Connectedtothis,theageoftheUniverseturnedouttobemoreuncertainthanhadbeenbelieved.20.1.2.Extragalacticdistancescale:Themeasurementofcosmologicaldistancestraditionallyemploysdistanceladders,asshowninTable20.1.Thelistingswritteninitalicsindicatenewmethodswhichcircumventintermediaterungs.ThemostimportantmilestoneoftheladderistheLMCdistance,50kpc(m−M=18:5).Thecentury-oldCepheidperiod-luminosity(PL)relationisstillgivengreatweight,butrequiresafewlowerrungstocalibrateitszeropoint.TherefurbishmentoftheHSTachievedsucientresolutiontoresolveCepheidsintheVirgocluster[3].Now28nearbyspiralgalaxieswithin25MpcaregivendistancesmeasuredusingtheCepheidPLrelation[4].Atypicalrandomerroris4{5%(0.08{0.10mag),andthesystematicerror(fromphotometry)is5%(0.1mag)excludingtheuncertaintyoftheLMCdista