A Primer on the Physics of the Cosmic Microwave Background

The following sections are included:

• Preface

• Contents

The following sections are included:

• The blackbody spectrum and its physical implications

• A bit of history of CMB observations

• The entropy of the CMB and its implications

• The time evolution of the CMB temperature

• A quick glance to the Sunyaev-Zeldovich effect

• Cosmological parameters

The following sections are included:

• The Standard Cosmological Model (SCM)
  • Homogeneity and isotropy
  • Perfect barotropic fluids
  • General Relativity

• Friedmann-Lemaître equations

• Matter content of the SCM

• The future of the Universe

• The past of the Universe
  • Hydrogen recombination
  • Coulomb scattering: the baryon-electron fluid
  • Thompson scattering: the baryon-photon fluid

• Simplified numerical estimates

The following sections are included:

• The horizon problem

• The spatial curvature problem

• The entropy problem

• The structure formation problem

• The singularity problem

The following sections are included:

• The horizon and the flatness problems

• Classical and quantum fluctuations

• The entropy problem

• The problem of geodesic incompleteness

The following sections are included:

• Fully inhomogeneous Friedmann-Lemaître equations

• Homogeneous evolution of a scalar field

• Classification(s) of inflationary backgrounds

• Exact inflationary backgrounds

• Slow-roll dynamics

• Slow-roll parameters

The following sections are included:

• Decomposition of inhomogeneities in FRW Universes

• Gauge issues for the scalar modes

• Super-adiabatic amplification

• Quantum mechanical description of the tensor modes

• Spectra of relic gravitons

• Quantum state of cosmological perturbations

• Digression on different vacua

• Numerical estimates of the mixing coefficients

The following sections are included:

• Tensor Sachs-Wolfe effect

• Scalar Sachs-Wolfe effect

• Scalar modes in the pre-decoupling phase
  • Scale crossing and CMB initial conditions

• CDM-radiation system

• Adiabatic and non-adiabatic modes: an example

• Sachs-Wolfe plateau: mixture of initial conditions

The following sections are included:

• The general plasma with four components

• CDM component

• Tight-coupling between photons and baryons

• Shear viscosity and silk damping

• The adiabatic solution

• Pre-equality non-adiabatic initial conditions
  • The CDM-radiation mode
  • The baryon-entropy mode
  • The neutrino-entropy mode

• Numerics in the tight-coupling approximation
  • Interpretation of the numerical results
  • Numerical estimates of diffusion damping

The following sections are included:

• Collisionless Boltzmann equation

• Boltzmann hierarchy for massless neutrinos

• Brightness perturbations of the radiation field

• Evolution equations for the brightness perturbations
  • Visibility function

• Line of sight integrals
  • Angular power spectrum and observables

• Tight-coupling expansion

• Zeroth order in tight-coupling: acoustic oscillations
  • Solutions of the evolution of monopole and dipole
  • Estimate of the sound horizon at decoupling

• First order in tight-coupling: polarization
  • Improved estimates of polarization
  • Polarization power spectra

• Second order in tight-coupling: diffusion damping

• Semi-analytical approach to Doppler oscillations

The following sections are included:

• Minimally coupled scalar field
  • Gauge-invariant description
  • Curvature perturbations and scalar normal modes

• Spectral relations
  • Some slow-roll algebra
  • Tensor power spectra
  • Scalar power spectra
  • Consistency relation

• Curvature perturbations and density contrasts

• Hamiltonians for the scalar problem

• Trans-Planckian problems?
  • Minimization of canonically related Hamiltonians
  • Back-reaction effects

• How many adiabatic modes?

The following sections are included:

• Generalities on scalar gauge transformations

• The longitudinal gauge
  • Gauge-invariant generalizations

• The synchronous gauge
  • Evolution equations in the synchronous gauge
  • The adiabatic mode in the synchronous gauge
  • Entropic modes in the synchronous gauge

• Comoving orthogonal hypersurfaces

• Uniform density hypersurfaces

• The off-diagonal gauge
  • Evolution equations in the off-diagonal gauge

• Mixed gauge-invariant treatments

The following sections are included:

• Interacting fluids with bulk viscous stresses

• Evolution equations for the entropy fluctuations

• Specific physical limits

• Mixing between entropy and curvature perturbations

The following sections are included:

• Spectator fields in a fluid background

• Unconventional inflationary models

• Conventional inflationary models

The following sections are included:

• Appendix A: The Concept of Distance in Cosmology
  • The proper coordinate distance
  • The redshift
  • The distance measure
  • Angular diameter distance
  • Luminosity distance
  • Horizon distances
  • Few simple applications

• Appendix B: Kinetic Description of Hot Plasmas
  • Generalities on thermodynamic systems
  • Fermions and bosons
  • Thermal, kinetic and chemical equilibrium
  • An example of primordial plasma
  • Electron-positron annihilation and neutrino decoupling
  • Big-bang nucleosynthesis (BBN)

• Appendix C: Scalar Modes of the Geometry
  • Fluctuations of the Einstein tensor
  • Fluctuations of the energy-momentum tensor(s)
  • Fluctuations of the covariant conservation equations
  • Some algebra with the scalar modes

• Appendix D: Metric Fluctuations: Gauge-Independent Treatment
  • The scalar problem
  • The vector problem
  • The tensor problem
  • Inhomogeneities of the sources

• Bibliography

• Index