Constraints on Omega_B, Omega_m and h from MAXIMA and BOOMER(2)

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

theseobservations,seeLineweaver&Barbosa1998).RecentballoonexperimentsBOOMERANGandMAXIMAreportedCMBRanisotropymeasurementsatangularscalesbetween 10 and 10′(deBernardisetal.2000,Hananyetal.2000).Theseexperimentsobservednearly1%oftheskywithangularresolution 10′.Forboththeseexperimentsthecosmicvariancewassmallenough(owingtotheskycoverage)todeterminepreciselythepositionofthe rstDopplerpeak( 200)oftheCMBRanisotropies.BothBOOMERANGandMAXIMAresultsgavestrongevidencethat Total=1(deBernardisetal.2000,Hananyetal.2000),whichwasalreadyindicatedbyotherobservations(Netter eldetal.1997).

Whilethepositionofthe rstDopplerpeakgiveunambiguousevidenceaboutthegeometryoftheuniverse,determinationofothercosmologicalparametersismoredi cult.Thisisbecausevariationinseveraldi erentparametersgivethesamechangeinmeasuredanisotropies,e.g.theheightof rstDopplerpeakisnearlydegeneratein B,h, Λandns.Someofthisdegeneracycanbeliftedwiththemeasurementofanisotropiesatevensmallerangularscales.BOOMERANGandMAXIMAprobewithangularscalescorrespondingtomultipoles max {600,700},respectively,whichisuptoorbeyondtheexpectedpositionofthesecondDopplerpeak.Thoughtheresultsoftheseexperimentshavenotbeenableto ndthepositionofthesecondDopplerpeak,accuratemeasurementofanisotropiesatsuchangularscalesisexpectedtobreaksomeofthedegeneracywhichmeasurementsnearthe rstDopplerpeakalonecannot.

TheBOOMERANGandMAXIMAdatahavebeenusedtodeterminevariouscosmologicalparameters(Balbietal.2000,Ja eetal.2000,Langeetal.2000,Tegmark&Zaldarriaga2000).Combinedwithotherindependentmeasurementsofcosmologicalparameters(e.g.measurementof Bh2fromelementabundance,measurementofhfromnearbyobservationsorinferenceaboutthevaluesof Λand mfromtheSN1adata,etc.)thesedataareexpectedtoleadtoauniquepicture.However,owingtodegeneraciesinparameterestimation,thevalueofestimatedparametersandtheirerrorsdependsensitivelyonvariousassumptionrelatedtotheassumedallowedrangeofparameters,i.e.onthepriorsontheparameters.

Inthisletter,weperformalikelihoodanalysisontheband-powersreportedbytheMAXIMAandBOOMERANGexperiments.However,insteadofofdoingamultipleparameteranalysis,we xthevaluesofmostparametersfromotherconsiderations(andprejudices!)andthenattempttoestimatejustthreeparameters— B,h,and massumingweakpriorsontheirallowedvalues.Inthenextsection,weexplainourchoiceofparametersandthemethodweuseinbrief.Inthethirdsection,wepresentandsummariseourresults.

1.CosmologicalparametersandCMBRdata

Mostgenericmodelsofin ationaryscenariogivetwouniquepredictions: Total=1andns 1(seee.g.Steinhardt1995).The rstofthesepredicationsiscon rmedbyBOOMERANGandMAXIMA.TheanalysisofCOBE-DMRdataisconsistentwithns=1(Bennettetal1996,Bunn