ContentsIntroductionConcordance CosmologyThe Homogeneous UniverseFrom Primordial Fluctuations to Large-Scale StructureThe Cosmic Microwave BackgroundTemperature AnisotropyPolarization AnisotropyInflationProblems of Standard Big Bang CosmologySolution of the Big Bang ProblemsClassical DynamicsThe Quantum Origin of StructurePredictions for the CMBThe CMB as a High Energy ExperimentCurrent Observational ConstraintsConnecting Primordial Input with DataHistory of CMB ObservationsWMAP and Inflationary PhysicsFuture ProspectsConclusionsAcknowledgmentsReferencesCosmological Inflation: Theory and ObservationsDaniel Baumann∗Department of Physics, Harvard University, Cambridge, MA 02138, U.S.A. andCenter for Astrophysics, Harvard University, Cambridge, MA 02138, U.S.A.Hiranya V. Peiris†Institute of Astronomy, Cambridge University, Cambridge, CB3 0HA, U.K.In this article we review the theory of cosmological inflation with a particular focus on the beautifulconnection it provides between the physics of the very small and observations of the very large.We explain how quantum mechanical fluctuations during the inflationary era become macroscopicdensity fluctuations which leave distinct imprints in the cosmic microwave background (CMB). Wedescribe the physics of anisotropies in the CMB temperature and polarization and discuss how CMBobservations can be used to probe the primordial universe.Keywords: cosmology, theory, observations, inflation, cosmic microwave background.Contents1. Introduction 12. Concordance Cosmology 32.1. The Homogeneous Universe 32.2. From Primordial Fluctuationsto Large-Scale Structure 33. The Cosmic Microwave Background 43.1. Temperature Anisotropy 43.2. Polarization Anisotropy 64. Inflation 74.1. Problems of Standard Big Bang Cosmology 74.2. Solution of the Big Bang Problems 84.3. Classical Dynamics 84.4. The Quantum Origin of Structure 104.5. Predictions for the CMB 104.6. The CMB as a High Energy Experiment 115. Current Observational Constraints 115.1. Connecting Primordial Input with Data 115.2. History of CMB Observations 135.3. WMAP and Inflationary Physics 146. Future Prospects 157. Conclusions 16Acknowledgments 17References 17∗Electronic address: [email protected]†Electronic address: [email protected]. INTRODUCTIONThe discovery of the expansion of the universe1byEdwin Hubble in 1929 heralded the dawn of observa-tional cosmology. If we mentally rewind the expansion,we find that the universe was hotter and denser in itspast. In fact, at very early times the temperature washigh enough to ionize the material that filled the uni-verse. The universe therefore consisted of a plasma ofnuclei, electrons and photons, and the number densityof free electrons was so high that the mean free path forthe Thomson scattering of photons was extremely short.As the universe expanded, it cooled, and the mean pho-ton energy diminished. Eventually, at a temperature ofabout 3000◦K, the photon energies became too low tokeep the universe ionized. At this time, known as recom-bination, the primordial plasma coalesced into neutralatoms, and the mean free path of the photons increasedto roughly the size of the observable universe. This radia-tion has since traveled essentially unhindered through theuniverse, and provides a snapshot of the universe when itwas only 370, 000 years old. Now, 13.7 billion years later,the radiation has cooled to microwave frequencies and isobserved as the cosmic microwave background (CMB),the thermal afterglow of the Big Bang.To a very good approximation, the temperature of theCMB is uniform across the whole sky; moreover, it isthe most perfect black-body spectrum known, with amean temperature of¯T0= 2.725◦K as measured by theCOsmic Background Explorer (COBE) satellite2in 1992.The discovery of the CMB3, together with the black-bodynature of its frequency spectrum, was of fundamental im-portance to cosmology because it validated the idea of ahot Big Bang – i.e. the universe was hot and dense in thepast and has since cooled by expansion4. Equally impor-tant is the fact that the CMB has slight variations of onepart in 100,000 in its temperature5. The most accuratemeasurement of these fluctuations is by the WilkinsonMicrowave Anisotropy Probe (WMAP)6. The tempera-ture anisotropies reflect the primordial inhomogeneitiesarXiv:0810.3022v1 [astro-ph] 16 Oct 200823 minTime [years] 370,000 13.7 billion10 -34 sRedshift 026251,10010 4Energy 1 meV1 eV1 MeV10 15 GeVScale a(t) 10-?CMBlensingIaQSOLyαgravitational wavesB-mode polarization21 cmneutrinosrecombinationBBNreheatingInflationreionizationgalaxy formationdark energyLSSBAOdark agesFIG. 1: History of the universe. In this schematic we present key events in the history of the universe and their associatedtime and energy scales. We also illustrate several cosmological probes that provide us with information about the structureand evolution of the universe.Acronyms: BBN (Big Bang Nucleosynthesis), LSS (Large-Scale Structure), BAO (Baryon Acoustic Oscillations), QSO (Quasi-Stellar Objects; Quasars), Lyα (Lyman-alpha), CMB (Cosmic Microwave Background), Ia (Type Ia supernovae), 21cm (hy-drogen 21cm-transition).in the underlying density field that provided the seedsfor cosmological structure formation.But what created these primordial inhomogeneities?In this review we describe how, in the initial moments ofthe Big Bang, a period of exponential expansion calledinflation7,8,9might have caused the universe to expand byat least a factor of 1026in an infinitesimal time (∼ 10−33seconds)7,10,11,12. The expansion was driven by a hypo-thetical quantum field called the inflaton, which sourcednegative pressure and accelerated expansion. The physi-cal size of the universe grew so much that it became muchlarger than the distance that light could have traveledsince the Big Bang (i.e. our observable horizon). Anyinhomogeneities that preceded inflation were erased andthe universe became flat and smooth throughout our ob-servable patch, in the same way that the surface of theearth looks flat when viewed from a small aircraft, eventhough its global shape is spherical. However, the the-ory also predicts that tiny quantum mechanical fluctu-ations in the inflaton field resulted in the perturbationsimprinted on the CMB and the large scale distribution ofgalaxies. This is the currently dominant theory for thegeneration of the initial inhomogeneities.In this review, we aim to provide a mostly qualitativeintroduction