Elements of String Cosmology

Maurizio Gasperini0521868750, 9780521868754, 9780511335457

The standard cosmological picture of our Universe emerging from a ‘big bang’ leaves open many fundamental questions which string theory, a unified theory of all forces of nature, should be able to answer. The first book dedicated to string cosmology, it contains a pedagogical introduction to the basic notions of the subject. It describes the new possible scenarios suggested by string theory for the primordial evolution of our Universe. It discusses the main phenomenological consequences of these scenarios, stresses their differences from each other, and compares them to the more conventional models of inflation. The book summarises over 15 years of research in this field and introduces current advances. It is self-contained, so it can be read by astrophysicists with no knowledge of string theory, and high-energy physicists with little understanding of cosmology. Detailed and explicit derivations of all the results presented provide a deeper appreciation of the subject.

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Table of contents :
Half-title……Page 3
Title……Page 5
Copyright……Page 6
Dedication……Page 7
Contents……Page 9
Preface……Page 13
Acknowledgements……Page 15
Notation, units and conventions……Page 16
Reference……Page 17
1.1.1 Einstein equations……Page 19
1.1.2 Homogeneity and isotropy……Page 20
1.1.3 Perfect fluid sources……Page 25
1.1.4 Thermal equilibrium……Page 32
1.2.1 Standard kinematic problems……Page 38
1.2.2 de Sitter inflation……Page 43
1.2.3 Slow-roll inflation……Page 44
1.2.4 Initial singularity……Page 48
References……Page 53
2 The basic string cosmology equations……Page 55
2.1 Tree-level equations……Page 56
2.2 The Einstein-frame representation……Page 63
2.3 First-order α’ corrections……Page 70
2.3.1 Higher-order gravi-dilaton equations……Page 74
Appendix 2A Differential forms in a Riemannian manifold……Page 82
References……Page 88
3 Conformal invariance and string effective actions……Page 89
3.1 Strings in curved backgrounds and conformal anomalies……Page 90
3.2 Higher-curvature and higher-genus expansion……Page 102
Appendix 3A The massless multiplet of the bosonic string in Minkowski space……Page 109
3A.1 Classical closed string……Page 111
3A.2 Classical open string……Page 113
3A.3 Quantization……Page 115
3A.4 Open string spectrum……Page 118
3A.5 Closed string spectrum……Page 120
Appendix 3B Superstring models and effective actions……Page 122
3B.1 Fermionic boundary conditions……Page 126
3B.2 Classical constraints……Page 127
3B.3 Quantization……Page 129
3B.4 Type IIA and type IIB superstrings……Page 135
3B.5 Type I superstring……Page 139
3B.6 Heterotic superstrings……Page 142
References……Page 148
4 Duality symmetries and cosmological solutions……Page 150
4.1 Scale-factor duality and the pre-big bang scenario……Page 152
4.2 Duality with matter sources……Page 160
4.2.1 General integration of the lowest-order equations……Page 166
4.2.2 Asymptotic limits……Page 171
4.3 Global O(d, d) symmetry……Page 175
4.3.1 O(d, d) symmetry and matter sources……Page 178
4.3.2 General integration of the matrix equations……Page 184
4.3.3 Non-trivial solutions via duality transformations……Page 186
4.3.4 Non-Abelian duality……Page 189
Appendix 4A A non-local, general-covariant dilaton potential……Page 192
Appendix 4B Examples of regular and self-dual solutions……Page 199
References……Page 210
5 Inflationary kinematics……Page 212
5.1 Four different types of inflation……Page 213
5.2 Dynamical equivalence of super-inflation and accelerated contraction……Page 216
5.3 Horizons and kinematics……Page 220
References……Page 227
6 The string phase……Page 228
6.1 High-curvature fixed points of the string cosmology equations……Page 231
6.2 Strong coupling corrections and the curvature “bounce”……Page 241
6.3 String gas cosmology……Page 249
Appendix 6A Birth of the Universe in quantum string cosmology……Page 257
6A.1 Tunneling from the string perturbative vacuum……Page 261
6A.2 Operator ordering……Page 262
6A.3 Scattering of the wave function in minisuperspace……Page 264
6A.4 Antitunneling from the string perturbative vacuum……Page 266
References……Page 268
7 The cosmic background of relic gravitational waves……Page 271
7.1 Propagation of tensor perturbations……Page 272
7.1.1 Frame independence……Page 278
7.1.2 Canonical normalization……Page 280
7.2 Parametric amplification and spectral distribution……Page 284
7.2.1 Spectral amplitude……Page 289
7.2.2 Graviton production and spectral energy density……Page 294
7.2.3 Matching conditions……Page 299
7.3 Expected relic gravitons from inflation……Page 305
7.3.1 Phenomenological bounds on the graviton background……Page 312
7.3.2 Primordial gravitons from pre-big bang inflation……Page 317
7.4 Sensitivities and cross-correlation of gravitational detectors……Page 328
7.4.1 Correlated response of two detectors……Page 334
Appendix 7A Higher-derivative corrections to the tensor perturbation equations……Page 341
References……Page 349
8 Scalar perturbations and the anisotropy of the CMB radiation……Page 352
8.1 Scalar perturbations in a cosmological background……Page 353
8.1.1 Gauge-invariant variables……Page 358
8.1.2 Scalar perturbation equations……Page 366
8.1.3 Scalar field source……Page 369
8.1.4 Perfect fluid source……Page 372
8.1.5 Generalized comoving gauges……Page 377
8.1.6 Frame transformations……Page 379
8.2 The anisotropy spectrum of the CMB radiation……Page 380
8.2.1 Primordial spectrum and slow-roll inflation……Page 383
8.2.2 “Conservation” of the Bardeen spectrum……Page 388
8.2.3 Sachs–Wolfe effect……Page 390
8.2.4 Adiabatic initial conditions……Page 395
8.2.5 Isocurvature initial conditions……Page 397
8.2.6 The angular power spectrum……Page 398
8.3 Adiabatic metric perturbations from the string theory axion……Page 407
8.3.1 The curvaton mechanism……Page 412
8.3.2 Normalization of the Bardeen spectrum……Page 421
Appendix 8A Photon–dilaton interactions and cosmic magnetic fields……Page 426
Appendix 8B Seeds for the CMB anisotropy……Page 434
References……Page 442
9 Dilaton phenomenology……Page 446
9.1 Spectral intensity of a massive dilaton background……Page 447
9.1.1 Dilaton mass and couplings……Page 455
9.1.2 Light and weakly coupled dilatons……Page 462
9.2 Interaction with gravitational antennas……Page 463
9.2.1 Pattern functions for interferometric detectors……Page 467
9.2.2 Signal-to-noise ratio……Page 470
9.2.3 Non-relativistic backgrounds……Page 474
9.2.4 Signal enhancement for flat spectra……Page 478
9.3 Dilaton dark energy and late-time acceleration……Page 481
9.3.1 Saturation of the loop corrections……Page 483
9.3.2 The dragging and freezing regimes……Page 486
9.3.3 A numerical example……Page 490
Appendix 9A The common mode of interferometric detectors……Page 496
References……Page 500
10 Elements of brane cosmology……Page 502
10.1 Effective gravity on the brane……Page 505
10.1.1 Covariant projection on the brane……Page 508
10.2 Warped geometry and localization of gravity……Page 514
10.2.1 Short-range corrections……Page 524
10.3 Brane-world cosmology……Page 526
10.3.1 Inflation on the brane……Page 531
10.3.2 Induced gravity on the brane……Page 537
10.4 Ekpyrotic and cyclic scenario……Page 541
10.5 Brane–antibrane inflation……Page 551
References……Page 563
Index……Page 566