Classical and quantum cosmology

목차 (Table of Contents)

• CONTENTS
• 1 Introduction = 1
• 1.1 Micro from Macro = 1
• 1.2 Outline of the Topics = 4
• 1.3 About Citations = 6
• 1.4 Conventions = 6
• 1.5 Measure Units = 7
• References = 8
• 2 Hot Big Bang Model = 13
• 2.1 Cosmic Expansion and Cosmological Principle = 14
• 2.1.1 The Universe at Large Scales = 14
• 2.1.2 Friedmann–Lemaître–Robertson–Walker Background = 19
• 2.2 Einstein and Continuity Equations = 24
• 2.2.1 Energy Conditions = 26
• 2.3 Perfect Fluid = 27
• 2.3.1 Scalar Field = 30
• 2.4 Friedmann Equations = 31
• 2.5 Content of the Universe = 33
• 2.5.1 Dust and Radiation = 33
• 2.5.2 Hot Big Bang and the Big-Bang Problem = 36
• 2.5.3 Dark Energy and the cosmological Constant Problem = 39
• 2.5.4 Spatial Curvature and Topology = 43
• 2.6 An Obscure Big Picture = 44
• 2.7 Problems and Solutions = 46
• References = 58
• 3 Cosmological Perturbations = 63
• 3.1 Metric Perturbations = 64
• 3.1.1 Linearized Einstein Equations = 64
• 3.1.2 Gauge Invariance and Gauge Fixing = 66
• 3.1.3 Cosmological Horizons = 66
• 3.1.4 Separate Universe Approach = 68
• 3.2 Linear Tensor Perturbations = 70
• 3.2.1 Transverse-Traceless Gauge = 70
• 3.2.2 Equation of Motion = 71
• 3.2.3 Mukhanov–Sasaki Equation and Solution = 71
• 3.2.4 Discovery of Gravitational Waves = 74
• 3.3 Scalar Perturbations = 76
• 3.3.1 Non-linear Perturbations = 76
• 3.3.2 Non-linear Perturbations at Large Scales = 77
• 3.3.3 Linear Perturbations at Large Scales = 78
• 3.4 Gaussian Random Fields = 81
• 3.4.1 Power Spectrum = 82
• 3.4.2 Bispectrum and Trispectrum = 83
• 3.5 Problems and Solutions = 84
• References = 88
• 4 Cosmic Microwave Background = 91
• 4.1 Cosmic Background Radiation = 93
• 4.1.1 Boltzmann Equation and Spectral Distortions = 94
• 4.1.2 Last-Scattering Surface = 97
• 4.2 Temperature Anisotropies : Formalism = 97
• 4.2.1 Spherical Harmonics = 97
• 4.2.2 Gaussian Spectrum = 99
• 4.2.3 Ergodic Hypothesis and Cosmic Variance = 102
• 4.3 Temperature Power Spectrum = 104
• 4.3.1 What we Observe = 104
• 4.3.2 Angular Scales = 106
• 4.3.3 Sachs–Wolfe Plateau (` . 60) = 110
• 4.3.4 Acoustic Peaks (60 . ` . 1000) = 114
• 4.3.5 Damping Tail (` & 1000) = 117
• 4.3.6 Secondary Anisotropies = 118
• 4.4 Cosmological Parameters and Observational Constraints = 119
• 4.4.1 Shape of the Angular Spectrum and Parameters = 119
• 4.4.2 Primordial Spectra = 120
• 4.5 Polarization = 126
• 4.5.1 Formalism = 128
• 4.5.2 Spectra = 130
• 4.5.3 What we Observe = 131
• 4.6 Non-Gaussianity = 135
• 4.6.1 Bispectrum = 135
• 4.6.2 Trispectrum = 137
• 4.6.3 Physical Origin = 138
• 4.6.4 Current Estimates = 141
• 4.7 Problems and Solutions = 142
• References = 146
• 5 Inflation = 153
• 5.1 Problems of the Hot Big Bang Model = 154
• 5.1.1 Planck and GUT Scale = 155
• 5.1.2 Flatness Problem = 156
• 5.1.3 Horizon Problem = 157
• 5.1.4 Monopole Problem = 158
• 5.1.5 Primordial Seeds Problem = 159
• 5.2 Inflationary Mechanism = 159
• 5.2.1 Solution of the Flatness Problem = 160
• 5.2.2 Solution of the Horizon Problem = 161
• 5.2.3 Solution of the Monopole Problem = 163
• 5.2.4 Solution of the Primordial Seeds Problem = 163
• 5.3 Cold Big Bang = 163
• 5.3.1 Equation of State = 164
• 5.3.2 Chaotic Inflation = 165
• 5.3.3 Reheating = 167
• 5.3.4 Observable Inflation = 169
• 5.3.5 Timeline of the Early Universe = 170
• 5.4 Scalar Field: Background Dynamics = 171
• 5.4.1 Hamilton–Jacobi Formalism = 171
• 5.4.2 Slow-Roll Parameters = 172
• 5.4.3 Inflationary Attractor = 176
• 5.5 Models of Inflation = 178
• 5.5.1 Large-Field Models = 179
• 5.5.2 Small-Field Models = 183
• 5.5.3 Multi-field Inflation = 185
• 5.6 First Glimpse of the Quantum Universe = 187
• 5.6.1 Decoherence = 188
• 5.6.2 From Quantum Fields to Classical Spectra = 189
• 5.6.3 Choice of Vacuum = 191
• 5.6.4 Mukhanov–Sasaki Equation Revisited = 193
• 5.6.5 Eternal Inflation = 197
• 5.7 Cosmological Spectra = 198
• 5.7.1 Gaussianity = 198
• 5.7.2 Linear Tensor Perturbations = 199
• 5.7.3 Linear Scalar Perturbations = 200
• 5.7.4 Consistency Relations and Lyth Bound = 204
• 5.8 Non-Gaussianity = 205
• 5.8.1 Stochastic Inflation = 206
• 5.8.2 Multi-field Non-Gaussianity = 213
• 5.9 Observational Constraints on Inflation = 213
• 5.9.1 Temperature Spectra = 213
• 5.9.2 Polarization = 216
• 5.9.3 Non-Gaussianity = 217
• 5.10 Unsolved and New Problems = 218
• 5.10.1 Graceful Entry Problem = 218
• 5.10.2 Graceful Exit Problem = 219
• 5.10.3 Trans-Planckian Problem = 219
• 5.10.4 Naturalness or Model-Building Problem = 220
• 5.11 The Inflaton and Particle Physics = 221
• 5.11.1 Not Only Scalars = 221
• 5.11.2 Higgs Inflation = 222
• 5.12 Supersymmetry and Supergravity = 224
• 5.12.1 Global Supersymmetry = 225
• 5.12.2 Supergravity = 228
• 5.12.3 -problem = 229
• 5.12.4 Inflation in Supergravity = 230
• 5.13 Problems and Solutions = 237
• References = 239
• 6 Big-Bang Problem = 261
• 6.1 Spacetimes and Singularities = 262
• 6.1.1 Globally Hyperbolic Spacetimes = 262
• 6.1.2 Focusing Theorems = 265
• 6.1.3 Classifications of Singularities = 267
• 6.2 Singularity Theorems = 269
• 6.2.1 Hawking–Penrose Theorems = 269
• 6.2.2 Borde–Vilenkin Theorems = 272
• 6.2.3 Borde–Guth–Vilenkin Theorem = 273
• 6.2.4 An Undecided Issue = 275
• 6.3 BKL Singularity = 278
• 6.3.1 Tetrads and Bianchi Models = 278
• 6.3.2 Kasner Metric = 280
• 6.3.3 Generalized Kasner Metric = 282
• 6.3.4 Mixmaster Dynamics = 284
• 6.3.5 BKL Conjecture = 291
• 6.4 Problems and Solutions = 293
• References = 295
• 7 Cosmological Constant Problem = 301
• 7.1 The Problem in Field Theory = 302
• 7.1.1 Spontaneous Symmetry Breaking and Dynamical = 302
• 7.1.2 Zero-Point Energy and Higher Loops = 305
• 7.1.3 Supersymmetry and Supergravity = 308
• 7.2 Other Versions of the Problem and Strategies = 310
• 7.2.1 Broken Symmetries = 310
• 7.2.2 The 4 Puzzle = 311
• 7.2.3 UV or IR Problem? Strategies for a Solution = 313
• 7.3 Quintessence = 315
• 7.3.1 Tracking, Freezing and Thawing = 316
• 7.3.2 Periodic and Power-Law Potentials = 321
• 7.3.3 Exponential and Hyperbolic Potentials = 322
• 7.3.4 Inverse Power-Law Potential = 323
• 7.3.5 Other Potentials = 324
• 7.3.6 Quintessence and the Inflaton = 325
• 7.3.7 Summary = 326
• 7.4 Scalar-Tensor Theories = 327
• 7.4.1 Motivations = 328
• 7.4.2 Conformal Transformations = 328
• 7.4.3 Perturbations, Quantum Theory and Extended Inflation = 332
• 7.4.4 Cosmological Constant Problem = 333
• 7.4.5 Experimental Bounds and Chameleon Mechanism = 334
• 7.5 Higher-Order and Higher-Derivative Gravity Models = 336
• 7.5.1 Motivation and Ghosts = 336
• 7.5.2 General f(R) Action = 338
• 7.5.3 Palatini Formulation = 340
• 7.5.4 Form of f(R) = 340
• 7.5.5 Horndeski Theory and Extensions = 342
• 7.6 Other Approaches = 343
• 7.6.1 Varying Couplings = 343
• 7.6.2 Void Models = 344
• 7.6.3 Unimodular Gravity = 346
• 7.6.4 Analogue Gravity and Condensates = 348
• 7.7 Emergent Gravity = 351
• 7.7.1 Rindler Observer and Null Congruences = 352
• 7.7.2 Dynamics = 355
• 7.7.3 Holographic Equipartition = 356
• 7.7.4 Cosmological Constant Problem = 360
• 7.8 Problems and Solutions = 361
• References = 369
• 8 The Problem of Quantum Gravity = 389
• 8.1 Do We Need to Quantize Gravity? = 390
• 8.2 Perturbative Quantum Gravity = 392
• 8.2.1 Supergravity = 397
• 8.2.2 Effective Field Theory = 397
• 8.2.3 Resummed Quantum Gravity = 398
• 8.3 Approaches to Quantum Gravity = 400
• 8.4 Problems and Solutions = 402
• References = 402
• 9 Canonical Quantum Gravity = 407
• 9.1 Canonical Variables in General Relativity = 408
• 9.1.1 First-Order Formalism and Parity = 408
• 9.1.2 Hamiltonian Analysis = 414
• 9.1.3 Ashtekar–Barbero Variables = 424
• 9.1.4 ADM Variables = 426
• 9.2 Wheeler–DeWitt Equation = 428
• 9.2.1 Superspace and Quantization = 429
• 9.2.2 Semi-classical States = 432
• 9.2.3 Boundary Conditions = 437
• 9.3 Some Features of Loop Quantum Gravity = 439
• 9.4 Cosmological Constant Problem = 442
• 9.4.1 Chern–Simons State = 443
• 9.4.2 as a Condensate? = 447
• 9.5 Problems and Solutions = 451
• References = 459
• 10 Canonical Quantum Cosmology = 467
• 10.1 Mini-superspace = 468
• 10.1.1 Classical FLRW Hamiltonian = 469
• 10.2 Wheeler–DeWitt Quantum Cosmology = 471
• 10.2.1 de Sitter Solutions and Probability of Inflation = 473
• 10.2.2 Massless Scalar Field and Group Averaging = 476
• 10.2.3 Quantum Singularity = 480
• 10.2.4 Cosmological Constant and the Multiverse = 482
• 10.2.5 Perturbations and Inflationary Observables = 484
• 10.3 Loop Quantum Cosmology = 489
• 10.3.1 Classical FLRW Variables and Constraints = 490
• 10.3.2 Quantization and Inverse-Volume Spectrum = 493
• 10.3.3 Mini-superspace Parametrization = 495
• 10.3.4 Quantum Hamiltonian Constraint = 496
• 10.3.5 Models with Curvature or a Cosmological Constant = 500
• 10.3.6 Homogeneous Effective Dynamics = 501
• 10.3.7 Singularity Resolved? = 508
• 10.3.8 Lattice Refinement : Quantum Corrections Revisited = 510
• 10.3.9 Perturbations and Inflationary Observables = 516
• 10.3.10 Inflation in Other Approaches = 525
• 10.3.11 Is There a Bounce? = 526
• 10.4 Problems and Solutions = 528
• References = 531
• 11 Cosmology of Quantum Gravities = 543
• 11.1 Hausdorff and spectral dimension = 545
• 11.2 Asymptotic Safety = 547
• 11.2.1 Framework = 548
• 11.2.2 Cosmology = 551
• 11.3 Causal Dynamical Triangulations = 555
• 11.3.1 Framework = 555
• 11.3.2 Cosmology = 561
• 11.4 Spin Foams = 563
• 11.4.1 Framework = 563
• 11.4.2 Cosmology = 564
• 11.5 Group Field Theory = 569
• 11.5.1 Framework = 569
• 11.5.2 Cosmology = 572
• 11.6 Causal Sets = 584
• 11.6.1 Framework = 584
• 11.6.2 Cosmology = 588
• 11.7 Non-commutative Spacetimes = 591
• 11.7.1 Framework = 591
• 11.7.2 Cosmology = 593
• 11.8 Non-local Gravity = 596
• 11.8.1 Non-locality = 596
• 11.8.2 Framework = 599
• 11.8.3 Cosmology = 603
• 11.9 Comparison of Quantum-Gravity Models = 604
• References = 607
• 12 String Theory = 625
• 12.1 Bosonic String = 627
• 12.1.1 Classical Free Strings and Branes = 627
• 12.1.2 D-Branes = 631
• 12.1.3 Quantum Strings and Critical Dimension = 632
• 12.1.4 Interactions = 637
• 12.1.5 Low-Energy Limit = 638
• 12.1.6 String Field Theory = 640
• 12.2 Superstring = 642
• 12.2.1 Action = 643
• 12.2.2 Quantization = 645
• 12.2.3 Type-I Superstring = 646
• 12.2.4 Type-II Superstrings = 647
• 12.2.5 Interactions and Anomaly Cancellation = 648
• 12.2.6 Heterotic Superstrings = 649
• 12.2.7 Massless Spectra and Low-Energy Limits = 651
• 12.2.8 Branes = 653
• 12.2.9 Superstring Field Theory = 655
• 12.3 Compactification = 656
• 12.3.1 T-Duality = 656
• 12.3.2 Spontaneous Compactification = 658
• 12.3.3 Calabi–Yau Spaces and Orbifolds = 658
• 12.3.4 Cycles and Fluxes = 662
• 12.3.5 Moduli = 663
• 12.3.6 Stacking Branes = 668
• 12.3.7 Flux Compactification = 669
• 12.3.8 String Theory and the Standard Model = 671
• 12.3.9 Anti-de Sitter Vacua = 671
• 12.4 Dualities and M-Theory = 678
• 12.5 Problems and Solutions = 682
• References = 683
• 13 String Cosmology = 701
• 13.1 String Landscape = 703
• 13.1.1 de Sitter Vacua = 705
• 13.1.2 Cosmological Constant = 709
• 13.1.3 Open Problems = 714
• 13.2 Inflation in the Landscape = 715
• 13.2.1 Single-Field Inflation = 716
• 13.2.2 Large-Field Models and the Weak Gravity Conjecture = 718
• 13.2.3 Multi-field Inflation = 719
• 13.2.4 Moduli Problem and -Problem = 720
• 13.3 Size Moduli Inflation = 720
• 13.3.1 Large-Volume Inflation = 721
• 13.3.2 Volume-Modulus Inflation = 725
• 13.3.3 Fluxless Inflation = 727
• 13.4 Axion Inflation = 728
• 13.4.1 Racetrack Axion Inflation = 729
• 13.4.2 Axion Valley = 730
• 13.4.3 N-flation = 732
• 13.4.4 Aligned and Hierarchical Axion Inflation = 734
• 13.4.5 Monodromy Inflation = 735
• 13.4.6 Problems with Axion Inflation and Ways Out = 740
• 13.5 Slow-Roll D-Brane Inflation = 742
• 13.5.1 Early Brane-Inflation Models = 742
• 13.5.2 Warped D-Brane Inflation and KLMT Model = 744
• 13.5.3 Cosmological KLMT Dynamics = 748
• 13.5.4 Refinements and Related Models = 750
• 13.5.5 Why the Tensor Spectrum Is Small = 753
• 13.6 DBI Inflation = 754
• 13.6.1 Setting = 754
• 13.6.2 UV Model = 755
• 13.6.3 IR Model = 758
• 13.7 Other Models = 761
• 13.7.1 Braneworld = 761
• 13.7.2 Cosmological Tachyon = 765
• 13.7.3 Modified Gravity = 767
• 13.7.4 Non-local Models = 769
• 13.7.5 Pre-Big-Bang and Dilaton Cosmology = 770
• 13.7.6 String-Gas Cosmology = 772
• 13.7.7 Cyclic Ekpyrotic Universe = 776
• 13.8 Inflation and Alternatives : Compact Summary = 783
• 13.9 Big-Bang Problem = 786
• 13.9.1 Big Bang in String Theory = 786
• 13.9.2 Classical Billiards: Living with the Singularity = 788
• 13.9.3 Quantum Billiards: Avoiding the Singularity? = 792
• References = 795
• 14 Perspective = 823
• References = 826
• Index = 829