Constraints on Omega_B, Omega_m and h from MAXIMA and BOOMER(4)

发布时间:2021-06-08

We analyse the BOOMERANG and MAXIMA results in the context of models with $\Omega_{\rm Total} = 1$ and $n_s = 1$. We attempt to constrain three other parameters---$h$, $\Omega_B$, and $\Omega_m$---from these observations. We show that: (a) the value of $\O

insteadofband-powersfordoingthemaximumlikelihoodanalysis.Wedonotuseithere.However,whilequotingerrorswedonotusetheFishermatrixapproachwhichcangivemeaningfulresultsonlyfortheGaussiancase.Insteadwedirectlygivethecon dencelevelson χ2.

2.Results

OurresultsareshowninFigures1and2.Theχ2for22datapointsfromBOOMERANGandMAXIMAwiththree ttedparameters(i.e.19degreesoffreedom)is22.4,whichisanexcellent t

.003(Goodness-of- tprobability,Q=0.26).Thebest tvaluesand1σerrorsare: B=0.075+0

0.015,

.08+0.04h=0.62+0

0.02and m=0.86 0.21.Thebest tmodelalongwithBOOMERANGandMAXIMAdatapointsisshowninFigure3.

Therangeofallowedhisinfairagreementwiththemeasurementofhfromlocalobservations(forarecentsummaryoftheseresults,seePrimack2000).RecentSN1asuggestthatthatthe

.09+0.052universeis atwith Λ+ m=1with m=0.28+0

0.08 0.04(1σ).Thisiswithin χ=2ofthe

valueinferredbyouranalysis.

InFigure1weshowthecon dencelevelsinthe B–hplane.Theregionboundedbythecontourscorrespondto χ2≤2.3and χ2≤6.17,which,forGaussianerrors,correspondsto68%(1σ)and95.4%(2σ)fortwo-parameter ts.Wealsoshowthe95%regionallowedbyprimordialnucleosynthesisobservations(forarecentreviewseeTytleretal2000).Asseeninthe gure,theregionallowedbyCMBRobservationsisatvariancewiththepredictionsofprimordialnucleosynthesisatatleast95%level.Thisresultisinagreementwithotheranalysesonthesamedataset(Tegmark&Zaldarriaga2000,Ja eetal2000).

Theregioncorrespondingtooneandtwoσinthe m–hplaneisshowninFigure2.OurresultsshowthatthecurrentCMBRobservationsfavourauniversewithage≤11Gyrandareincompatiblewithauniverseofage≥12Gyrat 95%level.Thoughthisisonthelowersideoftheexpectedageoftheuniversefromestimatedagesofglobularclusters,etc.,thisisnotindisagreementwiththoseobservations(forarecentstatusreportseePrimack2000).Anotherimportantconstraintonthevaluesof mandhcomesfromtheshapeofthepowerspectrumofgalaxyclustering(seee.g.Bond1996).Theseobservations,withinthecontextofa atmodelwithcosmologicalconstant,give mh 0.25±0.05.Weplotthisregioninthe m–hplaneinFigure2.Ifwerequirethath≤0.75,asmostrecentmeasurementsofhsuggest(Primack2000),thenCMBRobservationsexcludetheregionrequiredtosatisfythegalaxyclusteringobservationsbymorethan95%con dencelevel.

Inconclusion,recentBOOMERANGandMAXIMAobservations,withinthecontextofsim-plestin ationarymodels( Total=1andns 1),imply:(1)toolargeaofvalueof Bh2tobecompatiblewithprimordialnucleosynthesisobservations,(2)anageofuniverset0≤12Gyr,and

(3)toolargeavalueof mhtobeinagreementwiththeshapeofthepowerspectrumofgalaxyclustering.Inviewofthis,itissafetoconcludethatthemodelswith Total=1andns=1areruledoutbytheseobservations.

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