more information - www.cambridge.org/9781107013957 NEUTRINO COSMOLOGY The role that neutrinos have played in the evolution of the Universe is one of the mostfascinatingresearchareasthathasstemmedfromtheinterplaysbetweencos- mology,astrophysicsandparticlephysics.Inthisself-containedbook,theauthors bringtogetherallaspectsoftheroleofneutrinosincosmology,spanningfromlep- togenesistoprimordialnucleosynthesis,andfromtheirroleinCMBandstructure formationtotheproblemoftheirdirectdetection. The book starts by guiding the reader through aspects of fundamental neutrino physics,thestandardcosmologicalmodelandstatisticalmechanicsintheexpand- ingUniverse,beforediscussingthehistoryofneutrinosinchronologicalorderfrom the very early stages until today. This timely book will interest graduate students and researchers in astrophysics, cosmology and particle physics, who work with eitheratheoreticalorexperimentalfocus. julien lesgourgues currentlyworksatEPFLinLausanneandintheTheory Division at CERN, Switzerland. His research is focused on cosmology and on the theoretical interpretation of cosmic microwave background and large scale structureastrophysicaldata. gianpiero mangano is a Senior Researcher in Theoretical Physics at INFN, Italy. His research interests cover several areas in cosmology, such as primordial nucleosynthesisandthephysicsofneutrinosintheearlyUniverse,andcosmolog- icalaspectsofnoncommutativespacetimesatthePlanckscale. gennaro miele isAssociateProfessorinTheoreticalPhysicsattheUniversity ofNaples‘FedericoII’,Italy.Hismainresearchinterestconcernscosmology,where hehasbeenworkingonprimordialnucleosynthesisandneutrinocosmology. sergio pastor is a Researcher in the Instituto de F´ısica Corpuscular, CSIC – UniversitatdeVale`ncia,Spain.Hismainresearchinterestsincludeneutrinophysics, in particular the study of their role in astrophysical and cosmological scenarios, andothertopicsinastroparticlephysics. NEUTRINO COSMOLOGY JULIEN LESGOURGUES E´colePolytechniqueFe´de´raledeLausanne(EPFL),Switzerland CERN,Switzerland CNRS–Universite´deSavoie,France GIANPIERO MANGANO IstitutoNazionalediFisicaNucleare(INFN),Italy GENNARO MIELE UniversityofNaplesFedericoII,Italy SERGIO PASTOR IFIC,CSIC–UniversitatdeVale`ncia,Spain cambridge university press Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,Sa˜oPaulo,Delhi,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9781107013957 (cid:2)C J.Lesgourgues,G.Mangano,G.Miele,S.Pastor2013 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2013 PrintedandboundintheUnitedKingdombytheMPGBooksGroup AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata Lesgourgues,Julien. Neutrinocosmology/JulienLesgourgues,E´colePolytechniqueFederaledeLausanne(EPFL),Switzerland, CERN,Switzerland,CNRS–UniversitedeSavoie,France,GianpieroMangano,IstitutoNazionalediFisica Nucleare(INFN),Italy,GennaroMiele,UniversityofNaples“FredericoII”,Italy,SergioPastor,CSIC– UniversitatdeValencia,Spain. pages cm Includesbibliographicalreferencesandindex. ISBN978-1-107-01395-7(hardback) 1.Neutrinos. 2.Neutrinoastrophysics. 3.Cosmology. I.Mangano,Gianpiero. II.Miele,Gennaro. III.Pastor,Sergio. IV.Title. QC793.5.N42L47 2013 539.7(cid:3)215–dc23 2012042364 ISBN978-1-107-01395-7Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto inthispublication,anddoesnotguaranteethatanycontentonsuch websitesis,orwillremain,accurateorappropriate. Contents Preface pageix 1 Thebasicsofneutrinophysics 1 1.1 TheelectroweakStandardModel 2 1.2 Spontaneoussymmetrybreakingandfermionmasses 5 1.3 Thebasicpropertiesofneutrinos:interactions,masses andoscillations 9 1.3.1 Neutrinointeractionsinthelowenergylimit 9 1.3.2 DiracandMajoranamasses 16 1.3.3 Theseesawmechanism 22 1.3.4 Flavouroscillationsinvacuum 25 1.3.5 Flavouroscillationsinmatter 30 1.4 Neutrinoexperiments 35 1.4.1 Oscillationexperimentsandthree-neutrinomixing 35 1.4.2 Oscillationexperimentsandsterileneutrinos 40 1.4.3 Neutrinomassscaleexperiments 42 1.4.4 DiracorMajorana?Neutrinolessdouble-β decay 46 1.5 Nonstandardneutrino–electroninteractions 50 2 OverviewoftheStandardCosmologicalModel 53 2.1 Thehomogeneousandisotropicuniverse 55 2.1.1 Thedynamicsofexpansion 55 2.1.2 Distancesintheuniverse 65 2.2 Statisticalmechanicsintheexpandinguniverse 70 2.2.1 TherelativisticBoltzmannequation 70 2.2.2 Whenequilibriumholds 80 2.3 Theexpansionstages 83 2.3.1 Inflation 83 v vi Contents 2.3.2 Radiationandmatterdomination 87 2.3.3 (cid:3)(ordarkenergy)domination 92 2.4 Afirstlookatphotonandneutrinobackgrounds 95 2.4.1 Photondecouplingandtheformation ofthecosmicmicrowavebackground 95 2.4.2 Thecosmicneutrinobackground 98 3 Neutrinosintheearlyages 106 3.1 Thebaryonnumberoftheuniverse 107 3.2 Sakharovconditions 109 3.3 C,CP,B,outofequilibriumandallthat 112 3.3.1 CandCPviolation 112 3.3.2 Baryonandleptonnumberviolation 113 3.3.3 Relatingbaryonandleptonnumbers 119 3.3.4 Theout-of-equilibriumdecayscenario 121 3.4 Basicsofleptogenesis 125 3.4.1 StandardleptogenesisandMajorananeutrinos 126 3.4.2 Leptogenesisandneutrinooscillation:Two right-handedneutrinos 131 4 NeutrinosintheMeVage 134 4.1 Neutrinodecoupling 135 4.2 Neutrinooscillationsintheexpandinguniverse 143 4.2.1 Effectivematterpotentials 143 4.2.2 Densitymatrixformalism 145 4.2.3 Flavouroscillationsandrelicneutrinodistortions 152 4.2.4 Flavouroscillationsandrelicneutrinoasymmetries 154 4.2.5 Active–sterileoscillations 160 4.3 BigBangnucleosynthesis 166 4.3.1 Neutron–protonchemicalequilibrium 170 4.3.2 Thenuclearnetwork 173 4.3.3 Light-elementobservations 176 4.3.4 Theoryvs.data 180 4.4 BoundsonneutrinopropertiesfromBigBangnucleosynthesis 181 4.4.1 Extrarelativisticdegreesoffreedom 183 4.4.2 Relicneutrinoasymmetries 185 4.4.3 Nonstandardneutrinoelectromagneticproperties andinteractions 189 4.4.4 SterileneutrinosandBigBangnucleosynthesis 193 Contents vii 5 Neutrinosinthecosmicmicrowavebackgroundepoch 198 5.1 Cosmicmicrowavebackgroundanisotropies 199 5.1.1 Overview 199 5.1.2 Perturbationequations 201 5.1.3 Adiabaticandisocurvaturemodes 208 5.1.4 Powerspectraandtransferfunctions 211 5.1.5 Acousticoscillations 213 5.1.6 Temperatureanisotropies 220 5.1.7 Polarizationanisotropies 233 5.1.8 Tensorperturbations 234 5.2 Neutrinoperturbations 236 5.2.1 Perturbationequations 236 5.2.2 Neutrinoisocurvaturemodes 240 5.2.3 Adiabaticmodeinthepresenceofneutrinos 242 5.2.4 Free-streaminglength 244 5.2.5 Linearevolutionofneutrinoperturbations 248 5.2.6 Practicalimplementationandapproximations 249 5.3 Effectsofneutrinosonprimarycosmicmicrowavebackground anisotropies 253 5.3.1 Howcandecoupledspeciesaffectthecosmic microwavebackground? 253 5.3.2 Effectsofmasslessneutrinos 255 5.3.3 Effectsofmassiveneutrinos 262 5.3.4 Effectsofinteractingneutrinos 266 5.4 Boundsonneutrinosfromprimarycosmic-microwave- backgroundanisotropies 267 5.4.1 Cosmicmicrowavebackgroundandhomogeneous cosmologydatasets 267 5.4.2 Neutrinoabundance 268 5.4.3 Neutrinomasses 271 6 Recenttimes:neutrinosandstructureformation 273 6.1 Linearmatterpowerspectrum 274 6.1.1 Neutrinolessuniversewithcolddarkmatter 275 6.1.2 Neutrinolessuniversewithcolddarkmatterand baryons 284 6.1.3 Impactofmasslessneutrinos 290 6.1.4 Impactofhotdarkmatter 293 6.1.5 Impactofwarmdarkmatter 312 viii Contents 6.2 Nonlinearmatterpowerspectrum 317 6.2.1 N-bodysimulations 317 6.2.2 Analyticapproaches 323 6.3 Impactofneutrinosonsecondarycosmicmicrowave backgroundanisotropies 324 6.3.1 LateintegratedSachs–Wolfeeffect 324 6.3.2 Cosmicmicrowavebackgroundlensing 327 6.4 Observingthelarge-scalestructure 328 6.4.1 Galaxyandclusterpowerspectrum 329 6.4.2 Clustermassfunction 331 6.4.3 Galaxyweaklensing 332 6.4.4 Cosmicmicrowavebackgroundlensing 334 6.4.5 Lymanalphaforests 334 6.4.6 21-cmsurveys 335 6.5 Large-scalestructureboundsonneutrinoproperties 335 6.5.1 Activeneutrinomasses 335 6.5.2 Neutrinoabundanceandlightsterileneutrinos 339 6.5.3 Nonstandardpropertiesofactiveneutrinos 342 6.5.4 Heavysterileneutrinos(warmdarkmatter) 344 7 Cosmologicalneutrinostoday 348 7.1 Theultimatedream:detectingcosmologicalneutrinos 349 7.1.1 Scatterings:G2 effectsaretoosmall 349 F 7.1.2 TheorderG interactionsandtheStodolskyeffect 350 F 7.1.3 Massiveneutrinosandβ-decayingnuclei 354 7.2 Beyondtheultimatedream:neutrinoanisotropiesinthesky 359 7.2.1 Neutrinolastscatteringsurface 359 7.2.2 Masslessneutrinos 359 7.2.3 Massiveneutrinos 360 References 362 Index 375