Big Bang Nucleosynthesis and Cosmological Constrai

arXiv:astro-ph/0108341v121Aug2001CERN-TH/2001-020BigBangNucleosynthesisandCosmologicalConstraintsonNeutrinoOscillationParametersDanielaKirilovaa,candMihailChizhovb,caInstituteofAstronomy,BulgarianAcademyofSciences,Sofia,BulgariabCentreofSpaceResearchandTechnologies,SofiaUniversity,Sofia,BulgariacTheoryDivision,CERN,Geneva,SwitzerlandAbstractWepresentareviewofcosmologicalnucleosynthesis(CN)withneutrinooscil-lations,discussingthedifferenteffectsofoscillationsonCN,namely:increaseoftheeffectivedegreesoffreedomduringCN,spectrumdistortionoftheoscillatingneutrinos,neutrinonumberdensitydepletion,andgrowthofneutrino–antineutrinoasymmetryduetoactive–sterileoscillations.Wediscusstheimportanceoftheseeffectsfortheprimordialyieldofhelium-4.Primordiallyproduced4Hevalueisobtainedinaselfconsistentstudyofthenucleonsandtheoscillatingneutrinos.Theeffectsofspectrumdistortion,depletionandneutrino–antineutrinoasymmetrygrowthonhelium-4productionareexplicitlycalculated.Anupdateofthecosmologicalconstraintsonactive–sterileneutrinooscillationsparametersispresented,givingthevalues:δm2(sin22ϑ)4≤1.5×10−9eV2forδm20,and|δm2|8.2×10−10eV2atlargemixinganglesforδm20.Accordingtotheseconstraints,besidestheactive–sterileLMAsolution,alsotheactive–sterileLOWsolutiontothesolarneutrinoproblemisalmosttotallyexcluded.1IntroductionCosmologicalnucleosynthesisistraditionallyusedasaprobeoftheconditionsoftheearlyUniverseatthenucleosynthesisepoch(T∼MeV).Concerningneutrinophysics,therequirementforaconcordancebetweenthetheoreticallypredictedandtheextractedfromobservationsprimordialabundancesoflightelements,constrainsneutrinocharac-teristics:mass,numberoflightspecies,degeneracy,decaywidthandmassofeventualheavydecayingneutrinos,neutrinooscillationparameters,possiblenewinteractions,etc.Ontheotherhand,thetopicofneutrinooscillationsiswithussincePontecorvo’shypothesisforthese[1]i.e.morethan40years.Neutrinooscillationsimplynon-zeroneutrinomassesandmixings,thereforepresentinganindicationofphysicsbeyondtheelectroweakstandardmodel.Recentlythepositiveindicationsofoscillationsobtainedfromthegreatestneutrinoexperiments(SuperKamiokande,SNO,Soudan2,LSND,etc.)1turnedthesubjectofneutrinooscillationsintooneofthehottestpointsofastrophysicsandneutrinophysics.Hence,itlookslikeappropriatetoprovideanupdatedreviewoftheinfluenceofneutrinooscillationsonCNandpresentthemostrecentcosmologicalconstraintsonneutrinooscillationsparameters.IncaseneutrinooscillationsarepresentintheprimordialplasmaoftheearlyUniverse,theymayleadtochangesinCN,dependingontheoscillationchannelsandthewaytheyproceed.Namely,theoscillationseffectdependsonthekindofoscillations(theycanberesonantornonresonant)andalsodiffersfortheequilibriumandnonequilibriumcases.Oscillationsmayinfluencenucleosynthesisthroughtheireffectson:neutrinoandantineu-trinonumberdensities,spectrum,neutrino-antineutrinoasymmetryandthenumberofneutrinospecies.InthenextsectionwewillprovideareviewofCNwithneutrinooscillations,discussingmainlyoscillationsinfluenceonCN.Inthelastsectionwewillpresentanupdateofthecosmologicalconstraintsonνe↔νsneutrinooscillationparametersanddiscusshowtheyconcernthesolutionstothesolarneutrinoproblem.1AllrecentdataofthesolarneutrinoexperimentsnamelyGallium,Chlorine,SuperKamiokande,SNO,sensitivetodifferentneutrinoenergy,pointtoawellpronounceddeficitofsolarneutrinosincontrastwiththetheoreticalpredictionsoftheStandardSolarModelfluxes.ThemeasuredratioofthemuonoverelectronneutrinofluxbyKamiokande,SuperKamiokande,IMBandSoudan2isconsiderablylowerthanthepredictedonefortheatmosphericneutrinos,resultantfromtheprimarycosmicrayscollisionswiththenucleiintheupperatmosphere.Moreover,azenith-angle-dependentdeficitofmuonneutrinoswasobserved.TheLSNDexperimenthasobservedelectronantineutrinoappearanceinafluxofmuonantineutrinosandelectronneutrinosinafluxofmuonneutrinos.Thesethreeneutrinoanomaliesarepreferablyexplainedintermsofneutrinooscillations,whichareabletoprovideanaturalmechanismforenergydependentandneutrinotypedependentsuppressionofneutrinofluxes.Thereexistseveralsolutionstothesolarneutrinoproblem:SmallMixingAngle(SMA),LargeMixingAngle(LMA),LOWandVacuumOscillations(VO)solutions,whichimplyneutrinomassdifferencesintherange:10−10−10−4eV2.Theatmosphericneutrinoanomalycanberesolvedbyoscillationswithmassdifferences10−3−10−2eV2.WhilefortheLSNDneutrinoexperiment,muchbiggermassdifference,oftheorderofeVisnecessary.22HistoricaloverviewofCNwithneutrinooscilla-tions2.1StandardBigBangNucleosynthesisForapreciseanalysisoftheoscillationseffectonCN,theelementthatisusedtraditionallyishelium-4,asfarasthemostreliableandabundantdatanowavailableareforthatelement.AccordingtothestandardBigBangNucleosynthesis(SBBN)theory4Heisaresultofacomplexnetworkofnuclearreactions,whichproceedafterthefreezingoftheneutron-to-protonration/p.Theabundanceoftheprimordiallyproducedmassfractionofhelium-4Yp∼2(n/p)f/(1+(n/p)f)dependsmostlyontwocompellingprocesses,determiningtheneutron-to-protonfreezingratio–(n/p)f,namelytheUniverse’scoolingrate,H(t)∼√geffT2andtheinteractionratesoftheweakprocesses,interchangingneutr