Dark Matter and Dark Energy Astrophysics and Space Science Library EDITORIALBOARD Chairman W.B.BURTON,NationalRadioAstronomyObservatory,Charlottesville,VA,USA [email protected] UniversityofLeiden,Leiden,TheNetherlands [email protected] F.BERTOLA,UniversityofPadua,Padua,Italy J.P.CASSINELLI,UniversityofWisconsin,Madison,USA C.J.CESARSKY,EuropeanSouthernObservatory,GarchingbeiMünchen,Germany P.EHRENFREUND,UniversityofLeiden,Leiden,TheNetherlands O.ENGVOLD,UniversityofOslo,Oslo,Norway A.HECK,StrasbourgAstronomicalObservatory,Strasbourg,France E.P.J.VANDENHEUVEL,UniversityofAmsterdam,Amsterdam,TheNetherlands V.M.KASPI,McGillUniversity,Montreal,Canada J.M.E.KUIJPERS,UniversityofNijmegen,Nijmegen,TheNetherlands H.VANDERLAAN,UniversityofUtrecht,Utrecht,TheNetherlands P.G.MURDIN,InstituteofAstronomy,Cambridge,UK F.PACINI,IstitutoAstronomiaArcetri,Firenze,Italy V.RADHAKRISHNAN,RamanResearchInstitute,Bangalore,India B.V.SOMOV,AstronomicalInstitute,MoscowStateUniversity,Moscow,Russia R.A.SUNYAEV,SpaceResearchInstitute,Moscow,Russia Forothertitlespublishedinthisseries,goto www.springer.com/series/5664 Sabino Matarrese • Monica Colpi Vittorio Gorini • Ugo Moschella Editors Dark Matter and Dark Energy A Challenge for Modern Cosmology Editors Sabino Matarrese Monica Colpi Dipartimento di Fisica G. Galilei Dipartimento di Fisica G. Occhialini Università degli Studi di Padova Università de Milano Bicocca Via Marzolo 8 Piazza della Scienza 3 35131 Padova 20126 Milano Italy Italy Vittorio Gorini Ugo Moschella Dipartimento di Fisica e Matematica Dipartimento di Fisica e Matematica Università dell’Insubria Università dell’Insubria Via Valleggio 11 Via Valleggio 11 22100 Como 22100 Como Italy Italy Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands In association with Canopus Academic Publishing Limited, 15 Nelson Parade, Bedminster, Bristol, BS3 4HY, UK www.springer.com and www.canopusbooks.com ISSN 0067-0057 ISBN 978-90-481-8684-6 e-ISBN 978-90-481-8685-3 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2011920807 © Canopus Academic Publishing Limited 2011 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written per- mission from the Publisher, with the exception of any material supplied specifically forthe purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover illustration: The planck one-year all-sky survey, printed with kind permission of © ESA, HFI and LFI consortia, July 2010 Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Contents Introduction................................................ xi PartI Cosmology 1 RelativisticCosmology ....................................... 3 NorbertStraumann 1.1 Introduction.............................................. 3 1.2 EssentialsofFriedmann–LemaîtreModels .................... 4 1.2.1 Friedmann–LemaîtreSpacetimes .................... 5 1.2.2 ThermalHistoryBelow100MeV .................... 13 1.2.3 Luminosity-RedshiftRelation ....................... 22 1.3 InflationaryScenario ...................................... 27 1.3.1 Introduction ...................................... 27 1.3.2 TheHorizonProblemandtheGeneralIdeaofInflation.. 27 1.3.3 ScalarFieldModels ............................... 33 1.4 CosmologicalPerturbationTheory........................... 37 1.4.1 Generalities ...................................... 38 1.4.2 ExplicitformoftheEnergy-MomentumConservation... 48 1.4.3 EinsteinEquations................................. 49 1.5 SomeApplicationsofCPT ................................. 55 1.5.1 NonrelativisticLimit............................... 56 1.5.2 Large-ScaleSolutions.............................. 57 1.5.3 SolutionforDust.................................. 59 1.5.4 ASimpleRelativisticExample ...................... 60 1.6 CPTforScalarFieldModels................................ 61 1.6.1 BasicPerturbationEquations........................ 62 1.6.2 ConsequencesandReformulations ................... 65 1.7 Quantization,PrimordialPowerSpectra ...................... 70 1.7.1 PowerSpectrumoftheInflatonField ................. 71 1.7.2 GenerationofGravitationalWaves ................... 80 v vi Contents 1.7.3 AppendixtoSection1.7:EinsteinTensorforTensor Perturbations ..................................... 89 1.8 TightCouplingPhase...................................... 90 1.8.1 BasicEquations................................... 91 1.8.2 AnalyticalandNumericalAnalysis...................105 1.9 GeneralRelativisticBoltzmannEquation .....................112 1.9.1 One-ParticlePhaseSpace,LiouvilleOperator..........112 1.9.2 TheGeneralRelativisticBoltzmannEquation..........116 1.9.3 GaugeTransformations.............................117 1.9.4 LiouvilleOperatorintheLongitudinalGauge..........117 1.9.5 BoltzmannEquationforPhotons.....................120 1.9.6 TensorContributionstotheBoltzmannEquation .......125 1.9.7 CollisionIntegralforThomsonScattering .............126 References.....................................................130 2 CosmologywithCosmicMicrowaveBackgroundandLarge-Scale StructureObservations ...................................... 133 LiciaVerde 2.1 Introduction..............................................133 2.2 CosmicMicrowaveBackgroundandOtherDataSets:Whathave weLearnedAboutCosmology? .............................135 2.2.1 TestingInflation:StatusandtheProspects.............139 2.2.2 BeyondtheStandardCosmologicalModel ............143 2.3 CMB:HowistheInformationExtracted? .....................145 2.3.1 Real-WorldEffects ................................146 2.3.2 Beam............................................147 2.3.3 SkyCut..........................................148 2.3.4 HowDoYouMakeaCMBMapintheFirstPlace? .....148 2.3.5 Foregrounds......................................150 2.3.6 EstimationoftheC ...............................153 (cid:2) 2.3.7 Likelihoods ......................................153 2.4 TheDarkSideofLarge-ScaleStructures......................154 2.4.1 BasicToolsforLarge-ScaleStructure.................155 2.4.2 WindowandSelectionFunction .....................162 2.4.3 WeightingSchemestoAccountforallthatandMore....163 2.4.4 Redshift-SpaceDistortions..........................164 2.4.5 Nonlinearitiesetc. ................................166 2.4.6 BaryonAcousticOscillations(BAO) .................169 2.5 Conclusions..............................................175 References.....................................................175 Contents vii 3 CosmologywithGravitationalLensing ......................... 177 AlanHeavens 3.1 Introduction..............................................177 3.2 BasicsofLensing .........................................178 3.2.1 TheBendAngle...................................178 3.2.2 TheLensEquation ................................179 3.2.3 GeneralThinLensMassDistributions ................182 3.3 DarkMatter..............................................185 3.3.1 2DMassSurfaceDensityReconstruction .............185 3.3.2 TestingtheNavarro–Frenk–WhiteProfileofCDM......188 3.4 CosmologicalLensing .....................................189 3.4.1 DistortionofLightBundles .........................190 3.4.2 LensingPotential..................................191 3.4.3 MatterPowerSpectrum ............................194 3.4.4 IntrinsicAlignments ...............................195 3.4.5 E/BDecomposition................................196 3.4.6 Results ..........................................198 3.5 Lensingin3D ............................................199 3.5.1 3DPotentialandMassDensityReconstruction.........199 3.5.2 Tomography......................................201 3.5.3 TheShearRatioTest...............................203 3.5.4 Full3DAnalysisoftheShearField ..................204 3.5.5 DarkEnergywith3DLensingMethods ...............206 3.6 DarkGravity .............................................208 3.6.1 GrowthRate......................................210 3.7 TheFuture...............................................211 3.8 Appendix:ThePropagationofLightthroughaWeaklyPerturbed Universe.................................................212 3.8.1 TheGeodesicEquation.............................212 References.....................................................214 4 CosmologywithNumericalSimulations......................... 217 LauroMoscardiniandKlausDolag 4.1 Introduction..............................................217 4.2 N-BodyCodes............................................218 4.2.1 TheModelEquations ..............................218 4.2.2 TheParticle–Particle(PP)Method ...................219 4.2.3 TheParticle–Mesh(PM)Method ....................221 4.2.4 TreeCodes.......................................224 4.2.5 HybridMethods...................................225 4.2.6 InitialConditionsandSimulationSetup...............226 4.2.7 CodeComparison .................................227 4.3 HydrodynamicalCodes ....................................228 4.3.1 TheModelEquations ..............................228 viii Contents 4.3.2 SmoothedParticleHydrodynamics(SPH) .............229 4.3.3 EulerianMethods .................................233 4.3.4 CodeComparison .................................234 4.3.5 ExtraGasPhysics .................................234 References.....................................................236 PartII DarkMatter 5 DarkMatterAstrophysics .................................... 241 GuidoD’Amico,MarcKamionkowski,andKrisSigurdson 5.1 Introduction..............................................241 5.2 AstrophysicalEvidence ....................................242 5.2.1 GalacticRotationCurves ...........................242 5.2.2 GalaxyClusters ...................................244 5.2.3 Cosmic MicrowaveBackgroundand Large-Scale Structure.........................................247 5.3 BasicPropertiesofDarkMatter .............................248 5.4 WeaklyInteractingMassiveParticles(WIMPs) ................250 5.4.1 WIMPFreezeoutinEarlyUniverse ..................250 5.4.2 DirectDetection ..................................253 5.4.3 Energeticν’sfromtheSun..........................255 5.4.4 CosmicRaysfromDMAnnihilation .................256 5.5 VariationsandAdditions ...................................261 5.5.1 EnhancedRelicAbundance .........................261 5.5.2 KineticDecoupling................................262 5.5.3 Particle Decay and Suppression of Small-Scale Power ...........................................262 5.5.4 DipoleDarkMatter................................264 5.5.5 GravitationalConstraints ...........................264 5.5.6 Electromagnetic-LikeInteractionsforDarkMatter?.....266 5.6 SomeOtherParticleDark-MatterCandidates ..................266 5.6.1 SterileNeutrinos ..................................267 5.6.2 Axions ..........................................268 5.7 Conclusions..............................................270 References.....................................................270 6 DarkMatter:theParticlePhysicsView ......................... 273 AntonioMasiero 6.1 Introduction..............................................273 6.2 TheStandardModelofParticlePhysics.......................276 6.2.1 TheHiggsMechanismandVectorBosonMasses.......278 6.2.2 FermionMasses...................................279 6.2.3 SuccessesandDifficultiesoftheSM .................280 6.3 TheDMProblem:ExperimentalEvidence ....................281 6.4 LeptonNumberViolationandNeutrinosasHDMCandidates ....282 Contents ix 6.4.1 NeutrinoMassesintheSMandBeyond...............282 6.4.2 ThermalHistoryofNeutrinos .......................283 6.4.3 HDMandStructureFormation ......................285 6.5 Low-energySUSYandDM.................................285 6.5.1 NeutralinosastheLSPinSUSYModels ..............285 6.5.2 NeutralinosintheMinimalSUSYStandardModel .....286 6.5.3 ThermalHistoryofNeutralinosandΩ ............288 CDM 6.6 ChangingtheExpansionRateinthePast......................288 6.6.1 GRasaFixedPoint...............................290 6.7 ImplicationsforDMintheCMSSM .........................292 References.....................................................292 7 DarkMatterDirectandIndirectDetection ...................... 295 AndreaGiuliani 7.1 Introduction..............................................295 7.1.1 DarkMatterattheVariousScales ....................296 7.1.2 TheNatureofDarkMatter..........................296 7.2 DirectDetectionofWIMPsviaScatteringoffOrdinaryMatter ...301 7.2.1 RateandFeaturesoftheWIMP-NucleusInteractions ...301 7.2.2 StatusoftheExperimentalSearchforWIMPs..........306 7.3 IndirectDetectionviaAnnihilationofDarkMatterParticles......317 7.3.1 IntroductiontoAnnihilationMechanismsandProducts..319 7.3.2 IndirectSearchExploitingtheAntimatterComponent inCosmicRays ...................................321 7.3.3 IndirectSearchwithγ-raysandNeutrinos .............322 7.4 Conclusions..............................................326 References.....................................................327 PartIII DarkEnergy 8 DarkEnergy:InvestigationandModeling....................... 331 ShinjiTsujikawa 8.1 Introduction..............................................331 8.2 ObservationalConstraintsonDarkEnergy ....................333 8.2.1 SupernovaeIaObservations.........................333 8.2.2 CMB............................................338 8.2.3 BAO ............................................341 8.3 CosmologicalConstant ....................................342 8.4 ModifiedMatterModels ...................................346 8.4.1 Quintessence .....................................346 8.4.2 k-Essence........................................351 8.4.3 CoupledDarkEnergy..............................354 8.4.4 UnifiedModelsofDarkEnergyandDarkMatter .......364 8.5 ModifiedGravityModels...................................366 8.5.1 f(R)Gravity......................................366 8.5.2 Gauss–BonnetDarkEnergyModels..................375