From Primordial Quantum Fluctuations to the Anisotropies of CMBR

Friedmann-Lemaître spacetimes......Page 7
Spaces of constant curvature......Page 8
Curvature of Friedmann spacetimes......Page 9
Einstein equations for Friedmann spacetimes......Page 10
Redshift......Page 11
Cosmic distance measures......Page 12
Theoretical redshift-luminosity relation......Page 16
Type Ia supernovas as standard candles......Page 20
Results......Page 22
Systematic uncertainties......Page 23
Thermal history below 100 MeV......Page 25
I Cosmological Perturbation Theory......Page 32
Decomposition into scalar, vector, and tensor contributions......Page 34
Decomposition into spherical harmonics......Page 35
Gauge transformations, gauge invariant amplitudes......Page 36
Parametrization of the metric perturbations......Page 37
Geometrical interpretation......Page 39
Scalar perturbations of the energy-momentum tensor......Page 40
Explicit form of the energy-momentum conservation......Page 43
Einstein equations......Page 44
Extension to multi-component systems......Page 54
Appendix to Chapter 1......Page 63
Some Applications of Cosmological Perturbation Theory......Page 72
Non-relativistic limit......Page 73
Large scale solutions......Page 74
Solution of (2.6) for dust......Page 76
A simple relativistic example......Page 77
II Inflation and Generation of Fluctuations......Page 79
Introduction......Page 80
The horizon problem and the general idea of inflation......Page 81
Scalar field models......Page 86
Slow-roll approximation......Page 89
Why did inflation start?......Page 91
Cosmological Perturbation Theory for Scalar Field Models......Page 92
Basic perturbation equations......Page 93
Consequences and reformulations......Page 96
Power spectrum of the inflaton field......Page 102
Power spectrum for power law inflation......Page 104
Power spectrum in the slow-roll approximation......Page 107
Power spectrum for density fluctuations......Page 110
Generation of gravitational waves......Page 111
Power spectrum for power-law inflation......Page 114
Slow-roll approximation......Page 115
Stochastic gravitational background radiation......Page 116
Appendix to Chapter 5: Einstein tensor for tensor perturbations......Page 120
III Microwave Background Anisotropies......Page 123
Basic equations......Page 128
Analytical and numerical analysis......Page 134
Horizon crossing......Page 135
Sub-horizon evolution......Page 139
Transfer function, numerical results......Page 140
One-particle phase space, Liouville operator for geodesic spray......Page 143
The general relativistic Boltzmann equation......Page 147
Perturbation theory (generalities)......Page 148
Liouville operator in the longitudinal gauge......Page 151
Boltzmann equation for photons......Page 155
Tensor contributions to the Boltzmann equation......Page 160
The complete system of perturbation equations......Page 162
Acoustic oscillations......Page 164
Formal solution for the moments l......Page 169
Angular correlations of temperature fluctuations......Page 172
Angular power spectrum for large scales......Page 173
Influence of gravity waves on CMB anisotropies......Page 176
Polarization......Page 183
Observational results and cosmological parameters......Page 186
Concluding remarks......Page 192
Random fields, power spectra, filtering......Page 193
Collision integral for Thomson scattering......Page 195
Ergodicity for (generalized) random fields......Page 199