Contents -- Preface -- Part I -- 1. Why CMB Physics? -- 1.1 The blackbody spectrum and its physical implications -- 1.2 A bit of history of CMB observations -- 1.3 The entropy of the CMB and its implications -- 1.4 The time evolution of the CMB temperature -- 1.5 A quick glance to the Sunyaev-Zeldovich effect -- 1.6 Cosmological parameters -- 2. From CMB to the Standard Cosmological Model -- 2.1 The Standard Cosmological Model (SCM) -- 2.1.1 Homogeneity and isotropy -- 2.1.2 Perfect barotropic fluids -- 2.1.3 General Relativity -- 2.2 Friedmann-Lema^itre equations -- 2.3 Matter content of the SCM -- 2.4 The future of the Universe -- 2.5 The past of the Universe -- 2.5.1 Hydrogen recombination -- 2.5.2 Coulomb scattering: the baryon-electron fluid -- 2.5.3 Thompson scattering: the baryon-photon fluid -- 2.6 Simplified numerical estimates -- Part II -- 3. Problems with the SCM -- 3.1 The horizon problem -- 3.2 The spatial curvature problem -- 3.3 The entropy problem -- 3.4 The structure formation problem -- 3.5 The singularity problem -- 4. SCM and Beyond -- 4.1 The horizon and the atness problems -- 4.2 Classical and quantum uctuations -- 4.3 The entropy problem -- 4.4 The problem of geodesic incompleteness -- 5. Essentials of Inationary Dynamics -- 5.1 Fully inhomogeneous Friedmann-Lema^itre equations -- 5.2 Homogeneous evolution of a scalar field -- 5.3 Classification(s) of inationary backgrounds -- 5.4 Exact inationary backgrounds -- 5.5 Slow-roll dynamics -- 5.6 Slow-roll parameters -- Part III -- 6. Inhomogeneities in FRW Models -- 6.1 Decomposition of inhomogeneities in FRW Universes -- 6.2 Gauge issues for the scalar modes -- 6.3 Super-adiabatic amplification -- 6.4 Quantum mechanical description of the tensor modes -- 6.5 Spectra of relic gravitons -- 6.6 Quantum state of cosmological perturbations -- 6.7 Digression on different vacua.

6.8 Numerical estimates of the mixing coefficients -- 7. The First Lap in CMB Anisotropies -- 7.1 Tensor Sachs-Wolfe effect -- 7.2 Scalar Sachs-Wolfe effect -- 7.3 Scalar modes in the pre-decoupling phase -- 7.3.1 Scale crossing and CMB initial conditions -- 7.4 CDM-radiation system -- 7.5 Adiabatic and non-adiabatic modes: an example -- 7.6 Sachs-Wolfe plateau: mixture of initial conditions -- 8. Improved Fluid Description of Pre-Decoupling Physics -- 8.1 The general plasma with four components -- 8.2 CDM component -- 8.3 Tight-coupling between photons and baryons -- 8.4 Shear viscosity and silk damping -- 8.5 The adiabatic solution -- 8.6 Pre-equality non-adiabatic initial conditions -- 8.6.1 The CDM-radiation mode -- 8.6.2 The baryon-entropy mode -- 8.6.3 The neutrino-entropy mode -- 8.7 Numerics in the tight-coupling approximation -- 8.7.1 Interpretation of the numerical results -- 8.7.2 Numerical estimates of di usion damping -- 9. Kinetic Hierarchies -- 9.1 Collisionless Boltzmann equation -- 9.2 Boltzmann hierarchy for massless neutrinos -- 9.3 Brightness perturbations of the radiation field -- 9.4 Evolution equations for the brightness perturbations -- 9.4.1 Visibility function -- 9.5 Line of sight integrals -- 9.5.1 Angular power spectrum and observables -- 9.6 Tight-coupling expansion -- 9.7 Zeroth order in tight-coupling: acoustic oscillations -- 9.7.1 Solutions of the evolution of monopole and dipole -- 9.7.2 Estimate of the sound horizon at decoupling -- 9.8 First order in tight-coupling: polarization -- 9.8.1 Improved estimates of polarization -- 9.8.2 Polarization power spectra -- 9.9 Second order in tight-coupling: diffusion damping -- 9.10 Semi-analytical approach to Doppler oscillations -- 10. Early Initial Conditions? -- 10.1 Minimally coupled scalar field -- 10.1.1 Gauge-invariant description.

10.1.2 Curvature perturbations and scalar normal modes -- 10.2 Spectral relations -- 10.2.1 Some slow-roll algebra -- 10.2.2 Tensor power spectra -- 10.2.3 Scalar power spectra -- 10.2.4 Consistency relation -- 10.3 Curvature perturbations and density contrasts -- 10.4 Hamiltonians for the scalar problem -- 10.5 Trans-Planckian problems? -- 10.5.1 Minimization of canonically related Hamiltonians -- 10.5.2 Back-reaction effects -- 10.6 How many adiabatic modes? -- Part IV -- 11. Surfing on the Gauges -- 11.0.1 Generalities on scalar gauge transformations -- 11.1 The longitudinal gauge -- 11.1.1 Gauge-invariant generalizations -- 11.2 The synchronous gauge -- 11.2.1 Evolution equations in the synchronous gauge -- 11.2.2 The adiabatic mode in the synchronous gauge -- 11.2.3 Entropic modes in the synchronous gauge -- 11.3 Comoving orthogonal hypersurfaces -- 11.4 Uniform density hypersurfaces -- 11.5 The off-diagonal gauge -- 11.5.1 Evolution equations in the off-diagonal gauge -- 11.6 Mixed gauge-invariant treatments -- 12. Interacting Fluids -- 12.1 Interacting fluids with bulk viscous stresses -- 12.2 Evolution equations for the entropy fluctuations -- 12.3 Specific physical limits -- 12.4 Mixing between entropy and curvature perturbations -- 13. Spectator Fields -- 13.1 Spectator fields in a fluid background -- 13.2 Unconventional inflationary models -- 13.3 Conventional inflationary models -- Appendix A The Concept of Distance in Cosmology -- A.1 The proper coordinate distance -- A.2 The redshift -- A.3 The distance measure -- A.4 Angular diameter distance -- A.5 Luminosity distance -- A.6 Horizon distances -- A.7 Few simple applications -- Appendix B Kinetic Description of Hot Plasmas -- B.1 Generalities on thermodynamic systems -- B.2 Fermions and bosons -- B.3 Thermal, kinetic and chemical equilibrium -- B.4 An example of primordial plasma.

B.5 Electron-positron annihilation and neutrino decoupling -- B.6 Big-bang nucleosynthesis (BBN) -- Appendix C Scalar Modes of the Geometry -- C.1 Fluctuations of the Einstein tensor -- C.2 Fluctuations of the energy-momentum tensor(s) -- C.3 Fluctuations of the covariant conservation equations -- C.4 Some algebra with the scalar modes -- Appendix D Metric Fluctuations: Gauge-Independent Treatment -- D.1 The scalar problem -- D.2 The vector problem -- D.3 The tensor problem -- D.4 Inhomogeneities of the sources -- Bibliography -- Index.