INFLATION AND STRING THEORY Thepasttwodecadeshaveseentransformativeadvancesincosmologyandstring theory. Observations of the cosmic microwave background have revealed strong evidence for a period of inflationary expansion in the very early universe, while newinsightsaboutcompactificationsofstringtheoryhaveledtoadeeperunder- standingofinflationinaframeworkthatunifiesquantummechanicsandgeneral relativity. Writtenbytwooftheleadingresearchersinthefield,thiscompleteandacces- sible volume provides a modern treatment of inflationary cosmology and its connections to string theory and elementary particle theory. After an up-to-date experimentalsummary,theauthorspresentthefoundationsofeffectivefieldthe- ory, string theory, and string compactifications, setting the stage for a detailed examination of models of inflation in string theory. Three appendices contain background material in geometry and cosmological perturbation theory, mak- ing this a self-contained resource for graduate students and researchers in string theory, cosmology, and related fields. Daniel Baumann is Reader in Theoretical Physics at the University of Cambridge. He earned his Ph.D. from Princeton University in 2008 and was a postdoctoralresearcheratHarvardUniversityandattheInstituteforAdvanced Study in Princeton. Liam McAllister is Associate Professor of Physics at Cornell University. He earned his Ph.D. from Stanford University in 2005 and was a postdoctoral researcher at Princeton University. CAMBRIDGE MONOGRAPHS ON MATHEMATICAL PHYSICS General Editors: P. V. Landshoff, D. R. Nelson, S. Weinberg † S.J.AarsethGravitational N-BodySimulations:ToolsandAlgorithms J.Ambjørn,B.DurhuusandT.JonssonQuantumGeometry:AStatisticalFieldTheory † Approach A.M.AnileRelativisticFluidsandMagneto-fluids: WithApplicationsinAstrophysics and PlasmaPhysics J.A.deAzc´arragaandJ.M.IzquierdoLieGroups,LieAlgebras,Cohomology andSome † ApplicationsinPhysics † O.Babelon,D.BernardandM.TalonIntroductiontoClassical IntegrableSystems † F.BastianelliandP.vanNieuwenhuizenPathIntegralsandAnomaliesinCurvedSpace D.BaumannandL.McAllisterInflationandStringTheory † V.BelinskiandE.VerdaguerGravitational Solitons † J.BernsteinKineticTheoryintheExpandingUniverse † G.F.BertschandR.A.BrogliaOscillationsinFiniteQuantumSystems † N.D.BirrellandP.C.W.DaviesQuantumFieldsinCurvedSpace K.Bolejko,A.Krasin´ski,C.HellabyandM-N.C´el´erierStructuresintheUniversebyExact Methods:Formation,Evolution,Interactions † D.M.BrinkSemi-Classical MethodsforNucleus–NucleusScattering † M.BurgessClassicalCovariantFields E.A.CalzettaandB.-L.B.HuNonequilibriumQuantumFieldTheory † S.CarlipQuantumGravityin2+1Dimensions † P.CartierandC.DeWitt-MoretteFunctionalIntegration: ActionandSymmetries J.C.CollinsRenormalization: AnIntroductiontoRenormalization, theRenormalization Group † andtheOperator-Product Expansion † P.D.B.CollinsAnIntroduction toReggeTheoryandHighEnergyPhysics † M.CreutzQuarks,GluonsandLattices † P.D.D’EathSupersymmetricQuantumCosmology J.Derezin´skiandC.G´erardMathematicsofQuantizationandQuantumFields F.deFeliceandD.BiniClassical MeasurementsinCurvedSpace-Times † F.deFeliceandC.J.SClarkeRelativity onCurvedManifolds nd † B.DeWittSupermanifolds, 2 edition † P.G.O.FreundIntroductiontoSupersymmetry † F.G.FriedlanderTheWaveEquationonaCurvedSpace-Time J.L.FriedmanandN.StergioulasRotatingRelativisticStars Y.FrishmanandJ.SonnenscheinNon-PerturbativeFieldTheory:FromTwoDimensional ConformalFieldTheorytoQCDinFourDimensions J.A.FuchsAffineLieAlgebrasandQuantumGroups:AnIntroduction, withApplications in † ConformalFieldTheory J.FuchsandC.SchweigertSymmetries,LieAlgebrasandRepresentations: AGraduateCourse † forPhysicists † Y.FujiiandK.MaedaTheScalar-TensorTheoryofGravitation † J.A.H.Futterman,F.A.HandlerandR.A.MatznerScatteringfromBlackHoles † A.S.Galperin,E.A.Ivanov,V.I.OgievetskyandE.S.SokatchevHarmonicSuperspace † R.GambiniandJ.PullinLoops, Knots,GaugeTheoriesandQuantumGravity T.GannonMoonshinebeyondtheMonster:TheBridgeConnectingAlgebra,ModularFormsand † Physics † M.G¨ockelerandT.Schu¨ckerDifferentialGeometry,GaugeTheories,andGravity † C.G´omez,M.Ruiz-AltabaandG.SierraQuantumGroupsinTwo-DimensionalPhysics M.B.Green,J.H.SchwarzandE.WittenSuperstringTheoryVolume1:Introduction M.B.Green,J.H.SchwarzandE.WittenSuperstringTheoryVolume2:LoopAmplitudes, AnomaliesandPhenomenology V.N.GribovTheTheoryofComplexAngularMomenta:GribovLecturesonTheoretical † Physics † J.B.GriffithsandJ.Podolsky´ExactSpace-TimesinEinstein’sGeneralRelativity † S.W.HawkingandG.F.R.EllisTheLargeScaleStructureofSpace-Time † F.IachelloandA.ArimaTheInteractingBosonModel † F.IachelloandP.vanIsackerTheInteractingBoson-FermionModel C.ItzyksonandJ.M.DrouffeStatisticalFieldTheoryVolume1:FromBrownianMotionto † Renormalization andLatticeGaugeTheory C.ItzyksonandJ.M.DrouffeStatisticalFieldTheoryVolume2:StrongCoupling,MonteCarlo † Methods, ConformalFieldTheoryandRandomSystems G.JaroszkiewiczPrinciplesofDiscreteTimeMechanics † C.V.JohnsonD-Branes † P.S.JoshiGravitational CollapseandSpacetimeSingularities nd J.I.KapustaandC.GaleFinite-TemperatureFieldTheory:PrinciplesandApplications, 2 † edition V.E.Korepin,N.M.BogoliubovandA.G.IzerginQuantumInverseScatteringMethodand † CorrelationFunctions † M.LeBellacThermalFieldTheory † Y.MakeenkoMethods ofContemporary GaugeTheory † N.MantonandP.SutcliffeTopological Solitons † N.H.MarchLiquidMetals:ConceptsandTheory † I.MontvayandG.Mu¨nsterQuantumFieldsonaLattice † L.O’RaifeartaighGroupStructureofGaugeTheories nd T.Ort´ınGravityandStrings,2 edition † A.M.OzoriodeAlmeidaHamiltonianSystems:ChaosandQuantization L.ParkerandD.TomsQuantumFieldTheoryinCurvedSpacetime: QuantizedFieldsand Gravity R.PenroseandW.RindlerSpinorsandSpace-TimeVolume1:Two-SpinorCalculusand † RelativisticFields R.PenroseandW.RindlerSpinorsandSpace-TimeVolume2:SpinorandTwistorMethods in † Space-TimeGeometry nd † S.PokorskiGaugeFieldTheories,2 edition † J.PolchinskiStringTheoryVolume1:AnIntroduction totheBosonicString † J.PolchinskiStringTheoryVolume2:SuperstringTheoryandBeyond † J.C.PolkinghorneModelsofHighEnergyProcesses † V.N.PopovFunctionalIntegralsandCollectiveExcitations L.V.ProkhorovandS.V.ShabanovHamiltonianMechanicsofGaugeSystems A.RecknagelandV.SchomerusBoundaryConformalFieldTheoryandtheWorldsheetApproach toD-Branes † R.J.RiversPathIntegralMethodsinQuantumFieldTheory † R.G.RobertsTheStructureoftheProton:DeepInelasticScattering † C.RovelliQuantumGravity † W.C.SaslawGravitationalPhysicsofStellarandGalacticSystems R.N.SenCausality,MeasurementTheoryandtheDifferentiableStructureofSpace-Time M.ShifmanandA.YungSupersymmetricSolitons H.Stephani,D.Kramer,M.MacCallum,C.HoenselaersandE.HerltExactSolutionsof nd † Einstein’sFieldEquations,2 edition † J.StewartAdvancedGeneralRelativity † J.C.TaylorGaugeTheoriesofWeakInteractions † T.ThiemannModernCanonicalQuantumGeneralRelativity † D.J.TomsTheSchwingerActionPrincipleandEffectiveAction † A.VilenkinandE.P.S.ShellardCosmicStringsandOtherTopological Defects † R.S.WardandR.O.Wells,JrTwistor GeometryandFieldTheory E.J.WeinbergClassicalSolutionsinQuantumFieldTheory:SolitonsandInstantonsinHigh EnergyPhysics † J.R.WilsonandG.J.MathewsRelativisticNumericalHydrodynamics † Availableinpaperback Inflation and String Theory DANIEL BAUMANN University of Cambridge LIAM MCALLISTER Cornell University University PrintingHouse,Cambridge CB28BS,UnitedKingdom Cambridge University Pressis partof the University ofCambridge. Itfurthers the University’smissionby disseminating knowledge in thepursuit of education, learningand research atthe highest internationallevelsof excellence. www.cambridge.org Information onthis title: www.cambridge.org/9781107089693 (cid:2)c D. Baumann &L. McAllister 2015 Thispublication isin copyright.Subject tostatutoryexception andtothe provisions ofrelevant collectivelicensing agreements, no reproduction ofany partmay takeplacewithout thewritten permission of CambridgeUniversity Press. Firstpublished 2015 Printed inthe United Kingdomby Clays,St Ives plc A catalogue record for this publication is available from the British Library ISBN978-1-107-08969-3Hardback Cambridge UniversityPress has noresponsibility for the persistence or accuracy ofURLs for externalorthird-party internet websites referred tointhispublication, and does notguarantee thatany content on such websites is,orwillremain, accurate or appropriate. To Anna, Fritz, and Julian and to Josephine, Aelwen, and Vala