Paths to Dark Energy (eBook)

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Gene Byrd, University of Alabama, Tuscaloosa, USA; Arthur D. Chernin, Moscow State University, Russia; Pekka Teerikorpi and Mauri Valtonen,University of Turku, Finland.

Preface 5
1 The start of the paths 13
1.1 Newton’s absolute space and time 13
1.2 Light versus absolute space and time 14
1.3 Space-time events and intervals 16
1.4 Space-time measurements and Lorentz transformations 18
1.5 The Minkowski diagram 20
2 General Relativity: apparent acceleration of gravity 27
2.1 Gravitation as an apparent force 27
2.2 Principle of Equivalence 28
2.3 Lagrangians and motion of bodies 29
2.4 Integrals of motion 30
3 Tests of General Relativity 32
3.1 The Schwarzschild metric and the gravitational redshift 32
3.3 Orbits in General Relativity 36
3.2 Deflection of light 42
4 Curved space in cosmology 48
4.1 Non-Euclidean geometries 48
4.2 Curvature of 3-space 51
5 Finite versus infinite universe in space and time 61
5.1 Observation of an isotropic universe 61
5.2 A finite universe in time 61
5.3 The age of the universe via its “oldest objects” 62
5.4 Observational discovery of the expanding universe 66
5.5 Problems with the Hubble constant and the age of the universe 74
6 Cosmology and the “first appearance” of dark energy 78
6.1 A first formulation of dark energy: Einstein’s finite static universe 78
6.2 Cosmological redshift and Friedmann’s evolving universes 80
6.3 The Hubble constant in the Friedmann standard model 83
7 Einstein’s equations, criticai density and dark energy 89
7.1 Introduction 89
7.2 The path to Einstein equations with the cosmological constant 89
7.3 Interpretations of the cosmological constant 97
8 Modei Universes 100
8.1 Friedmann equation 100
8.2 The Einstein-de Sitter universe (critical density Friedmann case with no dark energy) 102
8.3 The de Sitter universe (introduction dark energy with no matter) 105
8.4 The Concordance Model (both matter and dark energy so k = 0) 105
8.5 Testing via the small scale Newtonian limit 109
8.6 Newtonian cosmology and the “k” parameter 112
9 Dark energy discovered 115
9.1 The era of zero-Lambda models 115
9.2 Cosmological angular-diameter distance estimates 116
9.3 Cosmological standard candle distance estimates 120
9.4 More luminous standard candles 121
9.5 Observational discovery of dark energy 124
9.6 Type Ia supernovae redshifts and distances vs uniform expansion 126
9.7 Could it be some problem with the standard candle method? 130
9.8 Modified gravity theories 132
10 Relics: cosmic microwave background (CMB) photons and neutrinos 135
10.1 The prediction and discovery of the CMB 135
10.2 The Big Bang components 136
10.3 The early radiation-dominated universe 139
10.4 Properties of cosmic microwave background radiation 142
10.5 Why a CMB thermal spectrum? 146
10.6 Relic neutrinos and O 157
11 Baryonic matter 160
11.1 Why matter and not also anti-matter? 160
11.2 Big Bang Nucleosynthesis prediction and processes 163
11.3 Baryon nucleosynthesis abundances and cosmological implications 165
11.4 The baryon content of cosmic systems 167
11.5 The Lyman alpha forest 168
12 Discovering dark matter 173
12.1 Dark matter in the Milky Way disk near the Sun 173
12.2 Dark matter discovery in clusters via the Virial Theorem 176
12.3 Subclusters in rich Clusters of galaxies 181
12.4 Dark matter discovery in Clusters via the Cluster gas 183
12.5 Dark matter in the Milky Way disk and its halo 187
12.6 Dark matter discovery inside disk galaxies via rotation curves 192
12.7 Dark matter discovery in the Local Group 194
12.8 Dark matter in binary Galaxy systems 197
12.9 Dark matter discovery via gravitational lensing 200
12.10 Dark matter in different scales 214
12.11 The importance and nature of dark matter versus baryonic matter 216
13 Dark matter and baryonic structures 218
13.1 Newton’s concept of gravitational instability 218
13.2 Basic hydrodynamics 219
13.3 Jeans Criterion 222
13.4 Jeans Criterion for collisionless dark matter gas 227
13.5 Jeans Criterion in the expanding universe 232
13.6 Evolution of density perturbations 238
13.7 Jeans mass in the early universe 241
13.8 Free streaming in dark matter 244
13.9 Dark matter perturbations 245
13.10 Dark matter drag 248
13.11 Termination of gravitational instability 249
13.12 Dark matter and baryonic structures 250
14 Dark energy and gravitating matter from structure in the universe 261
14.1 Introduction 261
14.2 Describing structure in the CMB radiation 261
14.3 The Power Spectrum 268
14.4 Perturbations of the gravitational potential 274
14.5 Harrison-Zeldovich spectrum of density perturbations 276
14.6 Perturbations and CMB 278
14.7 The cosmic horizon at CMB emission 280
14.8 The origin of peaks in CMB angular size spectrum 282
14.9 Cosmological parameters from CMB peaks: additional primary observations 285
14.10 Spatial Correlations of Galaxies 290
14.11 The CMB and the baryon acoustic oscillation (BAO) spectrum 298
14.12 The dark energy equation of state: is dark energy density a function of time? 302
14.13 Dark energy determined from gravitational lensing of the CMB 304
14.14 Cosmic 3D space: finite or infinite? 305
15 The local path to dark energy 312
15.1 A gravitating system within dark energy: the zero-gravity radius 312
15.2 Dynamical structure of a gravitating system within dark energy 317
15.3 Dark energy and determination of mass in systems of galaxies 321
15.4 Towards local measurement of dark energy 325
15.5 The Hubble law and dark energy 328
15.6 Redshift asymmetry as signature of dark energy 332
16 Cosmological inflation 340
16.1 Physics of the vacuum 340
16.2 Why does the universe expand? 344
16.3 Why is the universe uniform? 348
16.4 Scalar fields 351
16.5 Equation of motion 353
16.6 Reheating after inflation 356
16.7 Density perturbations and gravitational waves 356
17 Cosmic internal symmetry 358
17.1 Time-independent parameters of the Metagalaxy 358
17.2 The Friedmann integrals 360
17.3 The physics behind COINS 364
17.4 Coincidence problem 368
17.5 Dicke’s flatness problem and solutions 370
17.6 Big numbers 373
17.7 Extra dimensions? 374
17.8 New naturalness 380
17.9 Protogalactic perturbations 381
Bibliography 385
Index 406

lt;P>"The book has been edited in an attractive form. Numerous drawings, diagrams, photos, tables, gray boxes containing additional information, and also sparse problems excellently supplement the main material. Many chapters of the book can be read independently of each other. The book is addressed to a variety of readers, from graduate students to academic researchers who are not necessarily well acquainted with astrophysics and General Relativity." Mathematical Reviews

"A very interesting and comprehensive book, clearly written by four authors who tackle one of the most intriguing issues of modern astrophysics, the concept of dark matter and dark energy based on theory and observations. It presents to a reader a whole spectrum of facts and descriptions starting from historical introductions on how the gravity and related phenomena were first understood to the latest state of the art in the knowledge of cosmology obtained both by theoretical and observational means. The considered subjects are clearly described and explained, supplemented by standard mathematical derivations that can easily be followed even by those who are not strict specialists in these fields. In other words, the book is smoothly readable and can serve as a textbook for students, a reference book for researcher but also as a book the non-specialists can easily learn from." Zentralblatt für Mathematik