Cosmology

목차 (Table of Contents)

• CONTENTS
• Preface page = xiii
• Notation and Conventions = xvi
• Acknowledgments = xviii
• 1 Introduction = 1
• 1.1 Scales of the Universe = 1
• 1.2 The Invisible Universe = 3
• 1.3 The Hot Big Bang = 4
• 1.4 Growth of Structure = 7
• 1.5 Cosmic Palaeontology = 8
• Further Reading = 9
• Problems = 9
• Part I. The Homogeneous Universe
• 2 The Expanding Universe = 15
• 2.1 Geometry = 16
• 2.1.1 Spacetime and Relativity = 16
• 2.1.2 Symmetric Three-Spaces = 17
• 2.1.3 Robertson-Walker Metric = 19
• 2.2 Kinematics = 21
• 2.2.1 Geodesics = 21
• 2.2.2 Redshift = 26
• 2.2.3 Distances∗ = 29
• 2.3 Dynamics = 35
• 2.3.1 Perfect Fluids = 35
• 2.3.2 Matter and Radiation = 39
• 2.3.3 Dark Energy = 41
• 2.3.4 Spacetime Curvature = 44
• 2.3.5 Friedmann Equations = 47
• 2.3.6 Exact Solutions = 49
• 2.4 Our Universe = 57
• 2.5 Summary = 62
• Further Reading = 63
• Problems = 64
• 3 The Hot Big Bang = 70
• 3.1 Thermal Equilibrium = 72
• 3.1.1 Some Statistical Mechanics = 72
• 3.1.2 The Primordial Plasma = 74
• 3.1.3 Entropy and Expansion History = 82
• 3.1.4 Cosmic Neutrino Background = 85
• 3.1.5 Cosmic Microwave Background = 89
• 3.2 Beyond Equilibrium = 97
• 3.2.1 The Boltzmann Equation = 97
• 3.2.2 Dark Matter Freeze-Out = 99
• 3.2.3 Baryogenesis : A Sketch∗ = 103
• 3.2.4 Big Bang Nucleosynthesis = 107
• 3.2.5 Recombination Revisited∗ = 117
• 3.3 Summary = 124
• Further Reading = 126
• Problems = 127
• 4 Cosmological Inflation = 132
• 4.1 Problems of the Hot Big Bang = 133
• 4.1.1 The Horizon Problem = 133
• 4.1.2 The Flatness Problem = 137
• 4.1.3 Superhorizon Correlations = 138
• 4.2 Before the Hot Big Bang = 139
• 4.2.1 A Shrinking Hubble Sphere = 139
• 4.2.2 Horizon Problem Revisited = 140
• 4.2.3 Flatness Problem Revisited = 142
• 4.2.4 Superhorizon Correlations = 144
• 4.2.5 Duration of Inflation = 144
• 4.3 The Physics of Inflation = 146
• 4.3.1 Scalar Field Dynamics = 147
• 4.3.2 Slow-Roll Inflation = 150
• 4.3.3 Creating the Hot Universe = 153
• 4.4 Open Problems∗ = 154
• 4.4.1 Ultraviolet Sensitivity = 154
• 4.4.2 Initial Conditions = 156
• 4.4.3 Eternal Inflation = 158
• 4.5 Summary = 160
• Further Reading = 161
• Problems = 161
• Part II. The Inhomogeneous Universe
• 5 Structure Formation = 167
• 5.1 Newtonian Perturbation Theory = 168
• 5.1.1 Fluid Dynamics = 168
• 5.1.2 Adding Gravity = 170
• 5.1.3 Adding Expansion = 171
• 5.2 Growth of Matter Perturbations = 174
• 5.2.1 Jeans Instability = 174
• 5.2.2 Linear Growth Function = 175
• 5.2.3 Transfer Function = 178
• 5.3 Statistical Properties = 180
• 5.3.1 Correlation Functions = 180
• 5.3.2 Gaussian Random Fields = 182
• 5.3.3 Harrison-Zel’dovich Spectrum = 183
• 5.3.4 Matter Power Spectrum = 184
• 5.4 Nonlinear Clustering∗ = 185
• 5.4.1 Spherical Collapse = 186
• 5.4.2 Virialization and Halos = 189
• 5.4.3 A Bound on Lambda = 190
• 5.4.4 Press-Schechter Theory = 191
• 5.5 Summary = 198
• Further Reading = 200
• Problems = 200
• 6 Relativistic Perturbation Theory = 204
• 6.1 Linear Perturbations = 206
• 6.1.1 Metric Perturbations = 207
• 6.1.2 Matter Perturbations = 212
• 6.1.3 Conservation Equations = 217
• 6.1.4 Einstein Equations = 222
• 6.2 Initial Conditions = 226
• 6.2.1 Superhorizon Limit = 227
• 6.2.2 Adiabatic Perturbations = 229
• 6.2.3 Isocurvature Perturbations∗ = 230
• 6.2.4 Curvature Perturbations = 231
• 6.2.5 Primordial Power Spectrum = 233
• 6.3 Growth of Matter Perturbations = 234
• 6.3.1 Evolution of the Potential = 234
• 6.3.2 Clustering of Dark Matter = 237
• 6.3.3 Matter Power Spectrum = 240
• 6.4 Evolution of Photons and Baryons = 241
• 6.4.1 Radiation Fluctuations = 242
• 6.4.2 Photon-Baryon Fluid = 244
• 6.4.3 Cosmic Sound Waves = 245
• 6.5 Gravitational Waves = 249
• 6.6 Summary = 252
• Further Reading = 254
• Problems = 255
• 7 Cosmic Microwave Background = 259
• 7.1 Anisotropies in the First Light = 261
• 7.1.1 Angular Power Spectrum = 262
• 7.1.2 A Road Map = 264
• 7.2 Photons in a Clumpy Universe = 265
• 7.2.1 Gravitational Redshift = 265
• 7.2.2 Line-of-Sight Solution = 267
• 7.2.3 Fluctuations at Last-Scattering = 268
• 7.3 Anisotropies from Inhomogeneities = 271
• 7.3.1 Spatial-to-Angular Projection = 271
• 7.3.2 Large Scales : Sachs-Wolfe Effect = 274
• 7.3.3 Small Scales : Sound Waves = 275
• 7.4 Primordial Sound Waves = 276
• 7.4.1 Photon-Baryon Dynamics = 278
• 7.4.2 High-Frequency Solution = 279
• 7.4.3 Semi-Analytic Solution∗ = 282
• 7.4.4 Small-Scale Damping = 290
• 7.4.5 Summary of Results = 294
• 7.5 Understanding the Power Spectrum = 295
• 7.5.1 Peak Locations = 295
• 7.5.2 Peak Heights = 296
• 7.5.3 LCDM Cosmology = 299
• 7.5.4 Beyond LCDM = 305
• 7.6 A Glimpse at CMB Polarization∗ = 308
• 7.6.1 Polarization from Scattering = 308
• 7.6.2 Statistics of CMB Polarization = 310
• 7.6.3 Visualizing E- and B-modes = 315
• 7.6.4 E-modes from Scalars = 317
• 7.6.5 B-modes from Tensors = 324
• 7.7 Summary = 328
• Further Reading = 331
• Problems = 331
• 8 Quantum Initial Conditions = 336
• 8.1 Inflationary Perturbations = 337
• 8.1.1 Equation of Motion = 338
• 8.1.2 From Micro to Macro = 341
• 8.2 Quantum Fluctuations = 343
• 8.2.1 Quantum Harmonic Oscillators = 343
• 3 Primordial Power Spectra = 351
• 8.3.1 Curvature Perturbations = 352
• 8.3.2 Gravitational Waves = 354
• 8.3.3 Slow-Roll Predictions = 359
• 8.4 Observational Constraints∗ = 361
• 8.4.1 Current Results = 361
• 8.4.2 Future Tests = 365
• 8.5 Summary = 372
• Further Reading = 373
• Problems = 374
• 9 Outlook = 378
• Appendices
• Appendix A Elements of General Relativity = 379
• A.1 Spacetime and Relativity = 379
• A.2 Gravity Is Geometry = 388
• A.3 Motion in Curved Spacetime = 394
• A.4 The Einstein Equation = 403
• A.5 Summary = 414
• Further Reading = 415
• Appendix B Details of the CMB Analysis = 416
• B.1 Boltzmann Equation = 416
• B.2 Free Streaming and Projection = 422
• B.3 Evolution Before Decoupling = 424
• B.4 CMB Polarization = 431
• Appendix C Useful Quantities and Relations = 435
• C.1 Units and Conversions = 435
• C.2 Constants and Parameters = 437
• C.3 Important Relations = 439
• Appendix D Special Functions = 442
• D.1 Fourier Transforms = 442
• D.2 Spherical Harmonics = 442
• D.3 Legendre Polynomials = 443
• D.4 Spherical Bessel Functions = 444
• D.5 Bessel and Hankel Functions = 445
• D.6 Gamma and Zeta Functions = 446
• References = 447
• Index = 458