The Cosmic Microwave Background

by Ruth Durrer

• ISBN13: 9780521847049
• ISBN10: 0521847044
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-09-15
• Publisher: Cambridge University Press

Summary

The cosmic microwave background (CMB) is the radiation left over from the Big Bang. Recent analysis of the fluctuations in this radiation has given us valuable insights into our Universe and its parameters. Examining the theory of CMB and recent developments, this textbook starts with a brief introduction to modern cosmology and its main successes, followed by a thorough derivation of cosmological perturbation theory. It then explores the generation of initial fluctuations by inflation. The Boltzmann equation governs the evolution of CMB anisotropies and polarization is derived using the total angular momentum method. Cosmological parameter estimation and the lensing of CMB fluctuations and spectral distortions are also discussed. This textbook is the first to contain a full derivation of the theory of CMB anisotropies and polarization. Ideal for graduate students and researchers in this field, it includes end-of-chapter exercises, and solutions to selected exercises are provided.

Table of Contents

Preface	p. ix
The homogeneous and isotropic universe	p. 1
Homogeneity and isotropy	p. 2
The background geometry of the Universe	p. 3
Recombination and decoupling	p. 14
Nucleosynthesis	p. 27
Inflation	p. 42
Perturbation theory	p. 57
Introduction	p. 57
Gauge-invariant perturbation variables	p. 58
The perturbation equations	p. 70
Simple examples	p. 80
Light-like geodesics and CMB anisotropies	p. 87
Power spectra	p. 92
Final remarks	p. 102
Initial conditions	p. 105
Scalar field perturbations	p. 106
Generation of perturbations during inflation	p. 111
Mixture of dust and radiation revisited	p. 121
CMB anisotropies	p. 134
Introduction to kinetic theory	p. 134
The Liouville equation in a perturbed FL universe	p. 139
The energy-momentum tensor	p. 143
The ultra-relativistic limit, the Liouville equation for massless particles	p. 149
The Boltzmann equation	p. 156
Silk damping	p. 169
The full system of perturbation equations	p. 171
CMB polarization and the total angular momentum approach	p. 176
Polarization dependent Thomson scattering	p. 177
Total angular momentum decomposition	p. 183
The spectra	p. 188
The small-scale limit and the physical meaning of [epsilon] and B	p. 194
The Boltzmann equation	p. 199
Cosmological parameter estimation	p. 210
Introduction	p. 210
The physics of parameter dependence	p. 211
Reionization	p. 216
CMB data	p. 217
Statistical methods	p. 224
Degeneracies	p. 245
Complementary observations	p. 251
Sources	p. 265
Lensing and the CMB	p. 278
An introduction to lensing	p. 278
The lensing power spectrum	p. 282
Lensing of the CMB temperature anisotropies	p. 283
Lensing of the CMB polarization	p. 290
Non-Gaussianity	p. 300
Other second-order effects	p. 301
The CMB spectrum	p. 304
Collisional processes in the CMB	p. 304
A chemical potential	p. 318
The Sunyaev-Zel'dovich effect	p. 320
Fundamental constants, units and relations	p. 326
General relativity	p. 330
Perturbations	p. 335
Special functions	p. 340
Entropy production and heat flux	p. 357
Mixtures	p. 362
Statistical utensils	p. 364
Approximation for the tensor C[subscript l] spectrum	p. 370
Boltzmann equation in a universe with curvature	p. 375
The solutions of some exercises	p. 384
References	p. 392
Index	p. 399
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