Cosmological Crossroads : An Advanced Course in Mathematical, Physical and String Cosmology

An Advanced Course in Mathematical, Physical and String Cosmology

By: Spiros Cotsakis (Editor), Eleftherios Papantonopoulos (Editor)

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Hardcover | 1 December 2002

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Thisbookisaneditedversionofthelecturesdeliveredduringthe1stAegean SummerSchoolonCosmology, heldonSamosisland, Greece, inSeptember 21-29,2001, andorganizedjointlybytheDepartmentofMathematics, U- versity of the Aegean and the Department of Physics, National Technical UniversityofAthens. Cosmology, thescienceoftheuniverse, standsatthecrossroadsofmany ?eldsofphysicsandmathematicsandpresentsuswithchallengingproblems of many forms. Although there are by now many textbooks discussing the subjectatmanylevels, itistruethatnosinglebookhasthecharacteristics wehadinmindwheneditingthisvolume. Wehavetriednottoproducea proceedingsvolumebutmoreamultiauthoredtextbookwhichcouldserveas areferencesourceofcurrentideasincosmology. Webelievethisbookcovers atanintroductorylevelmostoftheissueswhichareconsideredimportant inmoderncosmologicalresearchandcanbereadbyagraduatestudentor researcherwhowishestoacquireareasonableknowledgeofcosmologythat will, wehope, continuetobeofvalueforyearstocome. The 1st Aegean School on Cosmology, and consequently this book, - camepossiblewiththekindsupportofmanypeopleandorganizations. We received ?nancial support from the following sources and this is gratefully acknowledged: the Municipality of Karlovassi, the North Aegean Regional Secretariat, the Prefecture of Samos, the Ministry of the Aegean, and the NationalBankofGreece. TheadministrativesupportoftheSchoolwastakenupwithgreatcare byMrs. EvelynPappaandMantoKatsianiandwewouldliketothankthem bothfortheirkinde?ortstoresolvemanyissueswhicharosebefore, during andaftertheSchool. WeacknowledgethehelpofMr. NectariosBenekoswho designedandmaintainedthewebsiteoftheSchool. Last, butnotleast, wearegratefultothesta?ofSpringer-Verlag, resp- siblefortheLectureNotesinPhysics, whoseabilitiesandhelpcontributed greatlytothe?neappearanceofthisbook. Karlovassi, Samos, SpirosCotsakis March2002 EleftheriosPapantonopoulos TableofContents PartI HistoryandOverview 1 IsNatureGeneric? SpirosCotsakis, PeterG. L. Leach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 2 PrinciplesofCosmologicalModelling. . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. 1 Spacetimes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. 2 TheoriesofGravity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 2. 3 MatterFields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 3 Cosmologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4 CosmologicalProblems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1. 4. 1 TheSingularityProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1. 4. 2 TheProblemofCosmicTopology. . . . . . . . . . . . . . . . . . . . . 9 1. 4. 3 TheProblemofAsymptoticStates. . . . . . . . . . . . . . . . . . . . 9 1. 4. 4 GravityTheoriesandtheEarlyUniverse. . . . . . . . . . . . . . . 11 1. 5Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 EvolutionofIdeasinModernCosmology AndreasParaskevopoulos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2. 2

Industry Reviews

"This book collects together a very nice set of introductions and overviews of important topics in Cosmology, covering current research and some older material, that would be difficult for many Cosmology or GR research groups to provide. Thus it would be very suitable for libraries that cannot acquire so many new publications, as well as for broadening the knowledge of graduate students and post-docs." (General Relativity and Gravitation, 35/11, 2003)

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Non-Fiction Science Physics Materials & States of Matter Mathematics Astronomy, Space & Time Cosmology & The Universe Applied Physics Astrophysics Relativity Physics Classical Mathematics Gravity

Medicine Medicine in General Geophysics Quantum Physics & Quantum Mechanics & Quantum Field Theory

History and Overview
Is Nature Generic?	p. 3
Introduction	p. 3
Principles of Cosmological Modelling	p. 4
Spacetimes	p. 4
Theories of Gravity	p. 5
Matter Fields	p. 6
Cosmologies	p. 6
Cosmological Problems	p. 8
The Singularity Problem	p. 8
The Problem of Cosmic Topology	p. 9
The Problem of Asymptotic States	p. 9
Gravity Theories and the Early Universe	p. 11
Outlook	p. 12
References	p. 14
Evolution of Ideas in Modern Cosmology	p. 16
Introduction	p. 16
The Beginnings of Modern Cosmology (1917-1950)	p. 17
Cosmology 1950-1970: Hot Big Bang, Singularities and Quantum Approach	p. 20
Cosmology 1970-1990: Chaotic, Inflationary, Quantum and Alternative	p. 22
Conclusions and Outlook	p. 25
References	p. 26
Mathematical Cosmology
Constraints and Evolution in Cosmology	p. 29
Introduction	p. 29
Moving Frame Formulas	p. 30
Frame and Coframe	p. 30
Metric	p. 31
Connection	p. 31
Curvature	p. 32
(n+1)-Splitting Adapted to Space Slices	p. 33
Definitions	p. 33
Structure Coefficients	p. 34
Splitting of the Connection	p. 34
Splitting of the Riemann Tensor	p. 35
Constraints and Evolution	p. 36
Analytic Cauchy Problem	p. 37
Non-strict Hyperbolicity of R_ij = 0	p. 38
Wave Equation for K, Hyperbolic System	p. 39
Hyperbolic-Elliptic System	p. 40
Local Existence and Uniqueness	p. 41
First Order Hyperbolic Systems	p. 41
FOSH Systems	p. 42
Other First Order Hyperbolic Systems	p. 42
Bianchi-Einstein Equations	p. 43
Wave Equation for the Riemann Tensor	p. 43
Case n=3, FOS System	p. 44
Cauchy Adapted Frame	p. 45
FOSH system for u = (E, H, D, B, &gmacr;, K, <$>bar {Gamma}}<$>)	p. 47
Elliptic - Hyperbolic System	p. 48
Bel-Robinson Energy	p. 49
Bel-Robinson Energy in a Strip	p. 49
Local Energy Estimate	p. 51
(n+1)-Splitting in a Time-Adapted Frame	p. 51
Metric and Coframe	p. 51
Splitting of Connection	p. 52
Splitting of Curvature	p. 53
Bianchi Equations (Case n=3)	p. 53
Vacuum Case	p. 54
Perfect Fluid	p. 54
Conclusion	p. 56
References	p. 57
Cosmological Singularities	p. 59
Introduction	p. 59
Cosmologies	p. 61
The Spacetime Metric	p. 65
Derivatives	p. 69
Transport and Geodesies	p. 74
Conjugate Points and Geodesic Congruences	p. 78
Causal Geometry	p. 83
Globalization and Singularity Theorems	p. 89
Cosmological Applications	p. 91
References	p. 93
Exact Cosmological Solutions	p. 95
Introduction: Mental Pictures of the Universe	p. 95
Basic Assumptions and Their Implications	p. 96
Assumptions	p. 96
Implications	p. 97
Homogeneous Isotropic Models	p. 98
Metric Forms	p. 98
Cosmological Redshift	p. 99
Evolution Equations and Sources	p. 100
Linear Equation of State	p. 101
Particular Models	p. 101
Standard Notation and the <$>Omega<$> - H Plane	p. 103
Homogeneous Anisotropic Models	p. 104
The Bianchi Classification	p. 105
Metric Forms	p. 105
Particular Models	p. 106
The Nature of the Initial Singularity	p. 108
Epilogue	p. 109
References	p. 109
Introduction to Cosmological Dynamical Systems	p. 111
Introduction	p. 111
One- and Two-Fluid Isotropic Cosmologies in GR	p. 111
Bianchi Models	p. 118
Scalar-Tensor Isotropic Cosmologies	p. 122
Appendix. Differential Equations. Basic Concepts	p. 126
Higher-Dimensional Systems	p. 130
Linearization	p. 135
Limit Sets, Invariant Sets	p. 138
Stability	p. 140
References	p. 143
Astrophysical and Observational Cosmology
The Quest for the Cosmological Parameters	p. 147
Background and Prerequisites	p. 147
Basic Elements of Dynamical Cosmology	p. 149
Thermal Beginning of the Universe	p. 151
Cosmological Parameters	p. 154
Distribution of Matter in the Universe	p. 158
Distance Scale, Hubble Constant and the Age of the Universe	p. 163
Distances of Extragalactic Objects	p. 164
Biases Affecting Distance Determinations	p. 166
Distance Indicators	p. 168
The Value of H_o and the Age of the Universe	p. 172
Determination of the Matter/Energy Density of the Universe	p. 175
The CMB Fluctuation Spectrum	p. 176
The Hubble Diagram with SNIa	p. 179
Clustering of Galaxies, Clusters and QSO's	p. 180
M/L Observations	p. 184
Cluster Baryon Fraction	p. 189
Large Scale Velocity Field	p. 190
Rate of Cluster Formation Evolution	p. 196
Summary	p. 200
References	p. 202
Modern Cosmological Observations	p. 208
Galaxies	p. 208
Introduction	p. 208
Some Cosmological Applications of Galactic Dynamics	p. 209
Redshift Surveys	p. 209
Number Counts and Galaxy Evolution	p. 210
High Redshift Galaxies	p. 210
Clusters and Groups of Galaxies	p. 211
Introduction	p. 211
Surveys for Clusters	p. 213
The Cosmological Significance of Clusters	p. 215
Active Galactic Nuclei	p. 216
Introduction	p. 216
AGN Surveys	p. 217
The AGN Evolution	p. 217
The AGN Clustering	p. 219
QSOs as a Probe of the Intergalactic Medium	p. 219
References	p. 220
Cosmological Perturbations	p. 223
Introduction	p. 223
Linear Newtonian Perturbations	p. 225
The General Fluid Equations	p. 226
The Unperturbed Background	p. 227
The Linear Regime	p. 228
The Jeans Length	p. 229
Multi-component Fluids	p. 230
Solutions	p. 231
Summary	p. 234
Linear Relativistic Perturbations	p. 234
The Gauge Problem	p. 235
The Relativistic Equations	p. 236
The Linear Regime	p. 238
Solutions	p. 239
Summary	p. 240
Baryonic Structure Formation	p. 241
Adiabatic and Isothermal Perturbations	p. 241
Evolution of the Sound Speed	p. 242
Evolution of the Jeans Length and the Jeans Mass	p. 243
Evolution of the Hubble Mass	p. 245
Dissipative Effects	p. 245
Scenarios and Problems	p. 247
Non baryonic Structure Formation	p. 250
Non-baryonic Cosmic Relics	p. 250
Evolution of the Jeans Mass	p. 251
Evolution of the Hubble Mass	p. 252
Dissipative Effects	p. 252
Scenarios, Successes and Shortcomings	p. 254
Discussion	p. 258
References	p. 260
Dark Matter: A Particle Theorist's Viewpoint	p. 262
Introduction	p. 262
Einstein Equations in a Friedmann-Robertson-Walker Universe	p. 262
The Hubble Constant - The Critical Density	p. 264
The Thermal Universe	p. 265
The Thermal Distributions of Particles	p. 265
The Energy Densities of Photons and Neutrinos	p. 267
The Evolution of the Universe	p. 268
Solving Friedmann's Equations	p. 268
"Decoupling" or "Freeze-out" of Particles	p. 270
Dark Matter	p. 272
Evidence for Dark Matter and Dark Energy	p. 272
Candidates for DM - Supersymmetry	p. 274
The Neutralino as the LSP and Its Relic Density	p. 277
The Neutralino as the LSP	p. 277
The Boltzmann Transport Equation	p. 278
Constraining SUSY - Conclusions	p. 282
References	p. 284
Particle and String Cosmology
An Introduction to Particle Physics	p. 287
The Standard Model	p. 287
Grand Unification	p. 293
Supersymmetry	p. 299
The Supersymmetric Standard Model	p. 304
Strings	p. 310
M-Theory and Duality	p. 315
References	p. 317
Quantum Cosmology	p. 318
Introduction	p. 318
Elements of Constrained Dynamics	p. 319
Introduction	p. 319
The Hamiltonian Approach	p. 319
Quantization of Constrained Systems	p. 323
A Pedagogical Example: The Kantowski-Sachs Model	p. 325
The Classical Case	p. 325
The Quantum Case	p. 328
Automorphisms in Classical and Quantum Cosmology	p. 329
The Simplification of Einstein's Equations	p. 329
Automorphisms, Invariant Description of 3-Spaces, and Quantum Cosmology	p. 335
References	p. 348
Inflationary Cosmology	p. 351
Introduction	p. 351
The Big Bang Model	p. 353
Hubble Expansion	p. 353
Friedmann Equation	p. 354
Important Cosmological Parameters	p. 356
Particle Horizon	p. 356
Brief History of the Early Universe	p. 357
Shortcomings of Big Bang	p. 358
Horizon Problem	p. 358
Flatness Problem	p. 359
Magnetic Monopole Problem	p. 359
Density Perturbations	p. 360
Inflation	p. 361
Resolution of the Horizon Problem	p. 362
Resolution of the Flatness Problem	p. 363
Resolution of the Monopole Problem	p. 363
Detailed Analysis of Inflation	p. 363
Coherent Oscillations of the Inflaton	p. 364
Decay of the Inflaton	p. 365
Density Perturbations from Inflation	p. 366
Density Perturbations in `Matter'	p. 369
Temperature Fluctuations	p. 370
Hybrid Inflation	p. 371
The Non-supersymmetric Version	p. 371
The Supersymmetric Version	p. 373
Extensions of Supersymmetric Hybrid Inflation	p. 376
Shifted Hybrid Inflation	p. 376
Smooth Hybrid Inflation	p. 379
`Reheating' and the Gravitino Constraint	p. 380
Baryogenesis via Leptogenesis	p. 382
Primordial Leptogenesis	p. 382
Sphaleron Effects	p. 384
Conclusions	p. 388
References	p. 388
String Cosmology	p. 392
Introduction	p. 392
Introduction to String Effective Actions	p. 394
World-Sheet String Formalism	p. 394
Conformal Invariance and Critical Dimension of Strings	p. 399
Some Hints Towards Supersymmetric Strings	p. 404
Kaluza-Klein Compactification	p. 405
Strings in Background Fields	p. 407
Conformal Invariance and Background Fields	p. 410
General Methods for Computing ß-Functions	p. 413
String Cosmology	p. 422
An Expanding Universe in String Theory and the Role of the Dilaton Background	p. 422
String Loop Corrections and De Sitter (Inflationary) Space Times	p. 431
De Sitter Universes and Pre-big Bang Scenaria: The Crucial Role of the Dilaton Field	p. 433
Some Phenomenological Implications of String Cosmology	p. 437
Challenges in String Cosmology and Speculations on Their Treatment	p. 439
Exit from Inflationary Phase: A Theoretical Challenge for String Theory	p. 439
Cosmological Backgrounds in String Theory and World-Sheet Renormalization-Group Flow	p. 442
Liouville Strings and Time as a World-Sheet RG Flow Parameter	p. 446
Liouville String Universe and Time-Dependent Vacuum Energy	p. 448
No Scattering Matrix for Liouville Strings	p. 449
Graceful Exit from Inflation in Liouville Strings	p. 451
Conclusions	p. 454
References	p. 455
Brane Cosmology	p. 458
Introduction	p. 458
A Surface Embedded in a D-Dimensional Manifold M	p. 460
Elementary Geometry	p. 460
The Embedding Procedure	p. 461
The Israel Matching Conditions	p. 463
Brane Cosmology in 5-Dimensional Spacetime	p. 464
The Einstein Equations on the Brane	p. 464
Cosmology on the Brane	p. 466
Induced Gravity on the Brane	p. 467
Cosmology on the Brane with a ⁽⁴⁾R Term	p. 468
A Brane on the Move	p. 469
Cosmology of the Moving Brane	p. 472
Conclusions	p. 473
References	p. 475
Table of Contents provided by Publisher. All Rights Reserved.

Cosmological Crossroads : An Advanced Course in Mathematical, Physical and String Cosmology

An Advanced Course in Mathematical, Physical and String Cosmology

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