String Cosmology: Modern String Theory Concepts from the Big Bang to Cosmic Structure

325 Pages·2009·2.93 MB·English

by  Johanna Erdmenger

StringCosmology
Editedby
JohannaErdmenger
Related Titles
Dvorak,R.(ed.) Roos,M.
ExtrasolarPlanets Introduction toCosmology
Formation,DetectionandDynamics
2003
2008 ISBN:978-0-470-84910-1
ISBN:978-3-527-40671-5
Shore,S.N.
Stern,A.,Mitton,J.
The Tapestryof Modern
Pluto and Charon
Astrophysics
IceWorldsontheRaggedEdge
oftheSolarSystem
2003
ISBN:978-0-471-16816-4
2005
ISBN:978-3-527-40556-5
Liddle,A.
Stahler,S.W.,Palla,F.
An IntroductiontoModern
TheFormation of Stars Cosmology
2004 2003
ISBN:978-3-527-40559-6 ISBN:978-0-470-84834-0
Foukal,P.V.
Solar Astrophysics
2004
ISBN:978-3-527-40374-5
String Cosmology
Modern String Theory Concepts
from the Big Bang to Cosmic Structure
Edited by
Johanna Erdmenger
WILEY-VCH Verlag GmbH & Co. KGaA
TheEditor AllbookspublishedbyWiley-VCHare
carefullyproduced.Nevertheless,authors,
Priv.-Doz.Dr.JohannaErdmenger editors,andpublisherdonotwarrantthe
Max-Planck-Institut informationcontainedinthesebooks,
fürPhysik includingthisbook,tobefreeoferrors.
FöhringerRing6D Readersareadvisedtokeepinmindthat
80805München statements,data,illustrations,procedural
detailsorotheritemsmayinadvertentlybe
inaccurate.
Cover LibraryofCongressCardNo.:appliedfor
Spieszdesign,Neu-Ulm BritishLibraryCataloguing-in-Publication
Data:Acataloguerecordforthisbookis
availablefromtheBritishLibrary.
Bibliographicinformationpublished
PortraitoftheEditor
bytheDeutscheNationalbibliothek
FotostudioSchönberger,
TheDeutscheNationalbibliothekliststhis
München
publicationintheDeutscheNationalbib-
liografie;detailedbibliographicdataare
availableontheInternetat
<http://dnb.d-nb.de>.
©2009WILEY-VCHVerlagGmbH&Co.
KGaA,Weinheim
Allrightsreserved(includingthoseof
translation into other languages).
Nopartofthisbookmaybereproduced
inanyformbyphotoprinting,microfilm,
oranyothermeansnortransmittedor
translatedintoamachinelanguagewithout
writtenpermissionfromthepublishers.
Registerednames,trademarks,etc.used
inthisbook,evenwhennotspecifically
markedassuch,arenottobeconsidered
unprotectedbylaw.
Typesetting le-texpublishingservicesoHG,
Leipzig
Printing StraussGmbH,Mörlenbach
Binding Litges&DopfGmbH,Heppenheim
PrintedintheFederalRepublicofGermany
Printedonacid-freepaper
ISBN 978-3-527-40862-7
V
Contents
Preface XI
1 IntroductiontoCosmologyandStringTheory 1
JohannaErdmengerandMartinAmmon
1.1 Introduction 1
1.2 FoundationsofCosmology 1
1.2.1 MetricandEinsteinEquations 2
1.2.2 EnergyContentoftheUniverse 4
1.2.3 DevelopmentoftheUniverse 6
1.3 Inflation 7
1.3.1 PuzzlesWithintheBigBangModel 7
1.3.2 TheConceptofInflation 7
1.4 Fluctuations 9
1.4.1 CharacterizationofSmallFluctuations 9
1.4.2 PowerSpectrum 10
1.4.3 FluctuationsandInflation 11
1.5 BosonicStringTheory 12
1.5.1 OpenandClosedStrings 14
1.5.1.1 ClosedStrings 15
1.5.1.2 OpenStrings 15
1.5.2 Quantization 16
1.5.3 StringPerturbationTheory:
InteractionsandScatteringAmplitudes 17
1.5.4 BosonicStringTheoryinBackgroundFields 19
1.5.5 Chan–PatonFactors 22
1.5.6 OrientedVersusUnorientedStrings 22
1.6 SuperstringTheory 23
1.6.1 TheRNSFormalismofSuperstringTheory 23
1.6.2 BoundaryConditionsforFermions 24
1.6.2.1 OpenStrings 24
1.6.2.2 ClosedString 25
1.6.3 TypeIIAandTypeIIBSuperstring 26
1.6.4 TypeISuperstring 26
StringCosmology.EditedbyJohannaErdmenger
Copyright©2009WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-40862-7
VI Contents
1.6.5 HeteroticSuperstring 27
1.7 StringDualitiesandM-Theory 28
1.7.1 Low-EnergyEffectiveActionofSuperstringTheory 28
1.7.2 T-Duality 29
1.7.2.1 T-DualityofClosedStrings 30
1.7.2.2 T-DualityofOpenStrings 31
1.7.2.3 T-DualityinSuperstringTheory 32
1.7.3 S-Duality 32
1.7.4 WebofDualitiesandM-Theory 33
1.7.4.1 TypeIIAStringTheoryandM-Theory 34
1.7.4.2 HeteroticE ~E StringTheoryandM-Theory 35
8 8
1.8 D-Branes 36
1.8.1 EffectiveActionofD-Branes 36
1.8.2 D-BranesasChargedBPSObjects 38
1.9 Compactification 38
1.9.1 StringTheoryonCalabi–YauManifolds 39
1.9.1.1 Low-EnergyEffectiveTheory 40
1.9.2 StringTheoryonOrbifolds 41
1.9.3 StringModuliandTheirStabilization 42
1.10 StringThermodynamics 43
1.11 Gauge–GravityDuality 44
1.12 Summary 45
References 45
2 StringInflationI:BraneInflation 47
MarcoZagermann
2.1 Introduction 47
2.1.1 InflationinStringTheoryandModuliStabilization 49
2.1.2 BraneInflationModels 50
2.1.3 TheRestofthisChapter 51
2.2 ModuliStabilizationinTypeIIBStringTheory 52
2.2.1 TypeIIBCalabi–YauOrientifoldsandTheirModuli 52
2.2.2 TheTree-LevelEffectiveAction 56
2.2.3 TheVolumeModulus 57
2.2.4 deSitterUplifting 58
2.3 WarpedD3/D3-BraneInflation(Slow-Roll) 59
2.3.1 TheWarpedThroatGeometry 61
2.3.2 TowardsSlow-RollInflation 61
2.3.3 VolumeStabilization 63
2.3.4 TheInflatonDependenceofW 64
2.4 D3/D7-BraneInflation 67
2.4.1 ACompactifiedExample 70
2.4.2 ModuliStabilization 71
2.5 DBIInflation 73
2.5.1 GeneralizingtheSlow-RollConditions 76
Contents VII
2.6 GravitationalWavesandInflatonFieldRange 77
2.6.1 D3-BranesonaSymmetricTorus 79
2.6.2 D3-BranesinaWarpedThroat 79
2.6.3 DBIInflation 80
2.6.4 WrappedBranes 81
2.6.5 OtherApproachesandRelatedWork 82
2.7 Conclusions 83
References 84
3 StringInflationII:InflationfromModuli 89
C.P.Burgess
3.1 Introduction 89
3.1.1 Closed-StringModuliasInflatons 90
3.1.2 ABriefRoadmap 91
3.1.3 JustifyingtheApproximations 92
3.2 AcceleratedExpansioninSupergravity 92
3.2.1 AcceleratedExpansioninHigherDimensions 92
3.2.2 Accelerationin4DSupergravity 93
3.3 TypeIIBModuliandTheirStabilization 94
3.3.1 Leading-OrderExpressions 94
3.3.2 CorrectionstotheLeadingApproximation 95
3.3.2.1 Leadingα(cid:1)Corrections 96
3.3.2.2 String-LoopCorrections 96
3.3.2.3 SuperpotentialCorrections 97
3.3.3 SupersymmetryBreakingPotentials 98
3.4 InflationfromKählerModuli 99
3.4.1 RacetrackInflation 100
3.4.2 Blow-UpModeInflation 103
3.4.3 FiberInflation 107
3.4.4 K3-FibrationCalabi–Yaus 107
3.4.5 TheScalarPotential 108
3.4.5.1 KineticTerms 111
3.4.5.2 InflationarySlowRoll 111
3.5 WhatWe’veLearnedsofar 116
References 118
4 CosmicSuperstrings 121
RobertC.MyersandMarkWyman
4.1 Introduction 121
4.1.1 SymmetryBreakingandTopologicalDefects 122
4.1.2 ABriefReviewofCosmic-StringNetworks 124
4.1.2.1 Small-ScaleStructure 126
4.2 SuperstringTheoryonCosmologicalScales 127
4.2.1 LowStringTensions? 129
4.2.2 StringsAfterInflation? 131
4.2.3 StabilityofCosmicSuperstrings? 134
VIII Contents
4.2.3.1 BreakageonSpace-FillingBranes 134
4.2.3.2 ConfinementbyAxionDomainWalls 136
4.2.3.3 “BaryonDecay” 136
4.2.3.4 TachyonCondensation 137
4.2.3.5 AnExample:TheKKLMMTModel 137
4.2.4 NovelPhysicsfromCosmicSuperstrings 140
4.2.4.1 PotentialProblemsforSuperstringNetworks 142
4.3 ObservingCosmicSuperstrings 143
4.3.1 ExperimentalLimitsandObservationalTests 144
4.3.1.1 CurrentLimits 144
4.3.1.2 SignaturesTestablebyNear-TermObservations 146
4.3.2 Novel Physics from Cosmic Superstrings: Observational Aspects
149
4.3.2.1 ReducedIntercommutationRates 149
4.3.2.2 Cosmic(p,q)-Strings 150
4.3.3 MonopolesandBeads 150
4.3.4 SemilocalStrings 151
4.3.5 MiscellaneousObservations 151
4.4 Conclusion 152
References 152
5 TheCMBasaPossibleProbeofStringTheory 157
GaryShiu
5.1 Introduction 157
5.2 StringTheoryandInflation 158
5.3 Example1:InitialStateofInflation 160
5.3.1 InitialStateEffectsintheCMBandTheirRelationtoNewPhysics
163
5.3.2 CorrectionstothePrimordialSpectrumfromScale-InvariantInitial
Conditions 165
5.3.3 CorrectionstothePrimordialSpectrumfromBoundaryEFT 165
5.3.4 ObservableParametersandPhysicalQuantities 167
5.4 Example2:Non-GaussianitiesintheCMB 169
5.4.1 The Shape of Non-Gaussianities and Experimental Constraints
173
5.5 Example3:ProbingtheShapeofExtraDimensions 177
5.5.1 TheWarpedDeformedConifoldandOtherWarpedThroats 178
5.5.2 ObservingWarpedGeometriesviatheCMB 182
5.6 SummaryandFutureDirections 186
References 188
6 StringGasCosmology 193
RobertH.Brandenberger
6.1 Introduction 193
6.1.1 Motivation 193
6.1.2 TheCurrentParadigmofEarlyUniverseCosmology 193
Contents IX
6.1.3 ChallengesforStringCosmology 195
6.1.4 Preview 197
6.2 BasicsofStringGasCosmology 197
6.2.1 PrinciplesofStringGasCosmology 197
6.2.2 DynamicsofStringGasCosmology 199
6.3 ModuliStabilizationinStringGasCosmology 203
6.3.1 Principles 203
6.3.2 StabilizationofGeometricalModuli 204
6.3.3 DilatonStabilization 207
6.4 StringGasCosmologyandStructureFormation 209
6.4.1 Overview 209
6.4.2 StringThermodynamics 212
6.4.3 SpectrumofCosmologicalFluctuations 217
6.4.4 SpectrumofGravitationalWaves 219
6.4.5 Discussion 221
6.5 Conclusions 222
References 225
7 Gauge–GravityDualityandStringCosmology 231
SumitR.Das
7.1 Introduction 231
7.2 NullSingularitiesandMatrixTheory 232
7.2.1 MatrixStringTheoryandMatrixMembraneTheory 232
7.2.1.1 MatrixStringTheory 232
7.2.1.2 MatrixMembraneTheory 235
7.2.2 MatrixBigBangs 236
7.2.2.1 IIBBigBangs 237
7.2.2.2 pp-WaveBigBangs 239
7.2.2.3 Issues 241
7.3 CosmologicalSingularitiesandtheAdS/CFTCorrespondence 242
7.3.1 Time-DependentSourcesinGaugeTheoryandTheirDualCosmologies
243
7.3.1.1 SolutionswithNullSingularities 243
7.3.1.2 SolutionswithSpace-LikeSingularities 245
7.3.1.3 Energy–MomentumTensors 247
7.3.1.4 GeneralPropertiesoftheDualGaugeTheory 248
7.3.1.5 TheWavefunctional 250
7.3.1.6 EnergyProduction 253
7.3.1.7 ParticleProduction 254
7.3.1.8 TheFateoftheSystem 255
7.3.1.9 Summary 256
7.3.2 AdSCosmologieswithUnstablePotentialsandTheirDuals 256
7.3.2.1 TheBulkCosmology 257
7.3.2.2 TheDualGaugeTheory 258
7.3.2.3 SelfAdjointExtensions 259