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The Cosmic Microwave Background:

The Cosmic Microwave Background

Publisher: Cambridge University Press | 424 pages | 2008-10-31 | 0521847044 | PDF | 1,5 Mb

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.

Contents
Preface page ix
1 The homogeneous and isotropic universe 1
1.1 Homogeneity and isotropy 2
1.2 The background geometry of the Universe 3
1.3 Recombination and decoupling 14
1.4 Nucleosynthesis 27
1.5 Inflation 42
2 Perturbation theory 57
2.1 Introduction 57
2.2 Gauge-invariant perturbation variables 58
2.3 The perturbation equations 70
2.4 Simple examples 80
2.5 Light-like geodesics and CMB anisotropies 87
2.6 Power spectra 92
2.7 Final remarks 102
3 Initial conditions 105
3.1 Scalar field perturbations 106
3.2 Generation of perturbations during inflation 111
3.3 Mixture of dust and radiation revisited 121
4 CMB anisotropies 134
4.1 Introduction to kinetic theory 134
4.2 The Liouville equation in a perturbed FL universe 139
4.3 The energy–momentum tensor 143
4.4 The ultra-relativistic limit, the Liouville equation for
massless particles 149
4.5 The Boltzmann equation 156
4.6 Silk damping 169
4.7 The full system of perturbation equations 171
5 CMB polarization and the total angular momentum approach 176
5.1 Polarization dependent Thomson scattering 177
5.2 Total angular momentum decomposition 183
5.3 The spectra 188
5.4 The small-scale limit and the physical meaning of E and B 194
5.5 The Boltzmann equation 199
6 Cosmological parameter estimation 210
6.1 Introduction 210
6.2 The physics of parameter dependence 211
6.3 Reionization 216
6.4 CMB data 217
6.5 Statistical methods 224
6.6 Degeneracies 245
6.7 Complementary observations 251
6.8 Sources 265
7 Lensing and the CMB 278
7.1 An introduction to lensing 278
7.2 The lensing power spectrum 282
7.3 Lensing of the CMB temperature anisotropies 283
7.4 Lensing of the CMB polarization 290
7.5 Non-Gaussianity 300
7.6 Other second-order effects 301
8 The CMB spectrum 304
8.1 Collisional processes in the CMB 304
8.2 A chemical potential 318
8.3 The Sunyaev–Zel’dovich effect 320
Appendix 1 Fundamental constants, units and relations 326
Appendix 2 General relativity 330
Appendix 3 Perturbations 335
Appendix 4 Special functions 340
Appendix 5 Entropy production and heat flux 357
Appendix 6 Mixtures 362
Appendix 7 Statistical utensils 364
Appendix 8 Approximation for the tensor C spectrum 370
Appendix 9 Boltzmann equation in a universe with curvature 375
Appendix 10 The solutions of some exercises 384
References 392
Index 399

[ 本帖最后由 drjiachen 于 2008-12-31 10:18 编辑 ]

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The Cosmic Microwave Background