Table of Contents
Preface ix
List of frequently used symbols xiii
1 Overview 1
2 Expansion history of the Universe 7
2.1 Friedmann equations 7
2.2 Hubble's law 12
2.3 Matter species in the Universe 13
2.4 Cosmic distances 18
2.5 The equation of state of dark energy 22
2.6 Problems 26
3 Correlation function and power spectrum 27
3.1 The correlation function 27
3.2 The n-point correlation function 30
3.3 The power spectrum 31
3.4 From the power spectrum to the moments 37
3.5 Problems 39
4 Basics of cosmological perturbation theory 40
4.1 Perturbing General Relativity 40
4.2 The Newtonian gauge 42
4.3 Single-fluid model 46
4.4 Scales larger than the horizon 51
4.5 Scales smaller than the Hubble radius 51
4.6 Two-fluid solutions 53
4.7 Velocity field 56
4.8 The redshift distortion 58
4.9 Baryons, photons, and neutrinos 62
4.10 The matter power spectrum 70
4.11 Perturbed photon propagation 76
4.12 Problems 83
5 Observational evidence of dark energy 84
5.1 The age of the Universe 84
5.2 Supernova observations 87
5.3 Cosmic Microwave Background 93
5.4 Baryon acoustic oscillations 102
5.5 Large-scale structure 106
5.6 Problems 108
6 Cosmological constant 109
6.1 Einstein equations with the cosmological constant 110
6.2 History of the cosmological constant 111
6.3 The fine tuning problem 113
6.4 The coincidence problem 114
6.5 Supersymmetric models 116
6.6 Cosmological constant and the anthropic principle 124
6.7 The decoupling of the cosmological constant from gravity 129
6.8 Problems 133
7 Dark energy as a modified form of matter I: Quintessence 134
7.1 Quintessence 135
7.2 Dynamical system approach 138
7.3 Early dark energy 149
7.4 Quintessence potentials in particle physics 153
7.5 Reconstruction of quintessence from observations 163
7.6 Problems 171
8 Dark energy as a modified form of matter II 172
8.1 k-essence 172
8.2 Phantoms 186
8.3 Coupled dark energy 189
8.4 Chameleon scalar fields 205
8.5 Dark energy models with scaling solutions 215
8.6 Unified models of dark energy and dark matter 225
8.7 Future singularities 230
8.8 Problems 233
9 Dark energy as a modification of gravity 234
9.1 f (R) gravity 234
9.2 Scalar-tensor theories 257
9.3 Gauss-Bonnet dark energy models 269
9.4 Braneworld models of dark energy 277
9.5 Problems 283
10 Cosmic acceleration without dark energy 285
10.1 Void models 286
10.2 Backreaction 292
10.3 Problems 295
11 Dark energy and linear cosmological perturbations 296
11.1 Perturbations in a general dark energy cosmology 296
11.2 Perturbations of a scalar field 306
11.3 From dark energy to dark force 309
11.4 A massive dark energy field 313
11.5 Sound speed of a scalar field 314
11.6 Perturbations in modified gravity models 317
11.7 Problems 335
12 Non-linear cosmological perturbations 336
12.1 Second-order perturbations 336
12.2 The bispectrum and the higher-order correction to the power spectrum 341
12.3 Spherical collapse 347
12.4 The mass function of collapsed objects 351
12.5 Dark energy N-body simulations 353
12.6 Problems 355
13 Statistical methods in cosmology 356
13.1 The likelihood function 356
13.2 Model selection 363
13.3 Fisher matrix 367
13.4 The Fisher matrix for the power spectrum 376
13.5 Principal component analysis 379
13.6 Problems 381
14 Future observational constraints on the nature of dark energy 383
14.1 Dark energy and the CMB 383
14.2 Large-scale structure 391
14.3 Growth function 398
14.4 Cosmic shear 403
14.5 Cluster abundances and baryon fraction 409
14.6 Other probes 415
14.7 Problems 426
15 Conculsion and outlook 427
16 Answers to the problems 430
17 Mathematical Appendix 455
References 457
Index 485
