Relativity and cosmology: from first principles to interpretations
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| Format: | Book |
| Language: | English |
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London ; San Diego ; Cambridge
Academic Press
[2025]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 239 Seiten Illustrationen, Diagramme |
| ISBN: | 9780443235429 |
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| 245 | 1 | 0 | |a Relativity and cosmology |b from first principles to interpretations |c Balša Terzić, Old Dominion University, Norfolk, VA, USA |
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Contents Preface хШ Acknowledgments xiv Organization of the book xvi Introduction 1 1. 2. 2 1.1. Motivation: Newton vs. Einstein 1.2. General relativity: a new theory of gravity 3 1.3. Book outline 4 Special relativity 2.1. 7 Newtonian (non-relativistic) physics 7 2.1.1. 2.1.2. 2.1.3. Inertial frames 7 Galilean transformations Crisis of Newtonian physics 8 10 2.2. Foundational premises of special relativity 2.3. Lorentz transformations 2.3.1. Standard configuration 2.3.2. Composition of velocities andgeneral Lorentz transformations 11 11 13 2.4. Length contraction 13 2.5. Time dilation 2.6. Invariance of the volume element 2.7. Timelike, spacelike, and null intervals 2.8. Recovering Newtonian mechanics: special limitv c 2.9. Covariant and contravariant four-vectors 2.9.1. Four-velocity . 10 14 14 15 16 17 19 2.10. Energy-momentum four-vector 20 2.11. Spacetime diagrams 22 2.12. Geodesics: equations of motion from an actionprinciple 25 2.13. What an observer observes 26 3. The Equivalence Principle 3.1. Newtonian gravity is inconsistent with specialrelativity 3.2. The equivalence of gravitational and inertial mass 3.2.1. 3.2.2. Light must also feel gravity Clocks in a uniform gravitational field 31 31 31 33 33 3.3. A scientific fable 35 3.4. Gravity as geometry 37 vii
viü Zements 3.5. 4. Geometric derivation of Newtonian gravity General relativity 41 4.1. Notation and conventions 41 4.2. General coordinate transformation 42 4.3. Spacetime coordinates and their metric tensors 44 4.4. 4.3.1. Symmetries of a metric tensor Metric tensors 46 47 4.4.1. 4.4.2. 4.4.3. Flat Euclidean space Flat Minkowski spacetime Curved spacetime 47 47 48 4.5. Freely falling frames 49 4.6. Area, volume, and four-volume 51 4.7. Vectors in curved spacetime 4.7.1. Coordinate bases 52 53 4.7.2. Orthonormal bases 54 4.8. Covariant derivative 57 4.9. Geodesic equation 58 4.9.1. 5. 38 Recovering Newtonian gravity Einstein's field equations 61 65 5.1. Bulk macroscopic description of matter: the Eulerian form 5.1.1. Conservation laws in flat spacetime 65 67 5.2. The energy ■ momentum tensor 68 5.3. The Riemann tensor, the Ricci tensor, the Ricci scalar,and the Einstein tensor 70 5.4. Evolution of energy density 5.4.1. Matter density 5.4.2. Radiation density 72 74 74 5.5. Einstein's field equations 6. The Schwarzschild metric and black holes 74 77 6.1. The Schwarzschild problem 77 6.2. Solving the Schwarzschild problem 78 6.3. Schwarzschild radius, event horizon, and black holes 83 6.4. Orbits in Schwarzschild's geometry 84 7. The cosmological metric and Friedmann's equations 87 7.1. Hubble's law and the evolving Universe 87 7.2. Friedmann's equations 91 7.3. A Newtonian analogy to Friedmann's equations 94
Contents 8. Solutions of Friedmann's equations 97 8.1. Cosmologicalmodels 8.1.1. Equation of state for the radiation-dominated Universe: perfect fluid 8.1.2. Equation of state for the matter-dominated Universe: dust 8.1.3. Curvature of the Universe 97 97 98 99 8.2. Flat Universe (k = 0, 70 = 1/2) 8.2.1. Radiation-dominated Universe (perfect-fluid approximation) 8.2.2. Matter-dominated Universe (dust approximation) 100 Closed Universe (k =+1, 70 1/2) 8.3.1. Radiation-dominated Universe (perfect-fluid approximation) 8.3.2. Matter-dominated Universe (dust approximation) 102 102 103 8.3. 8.4. 8.5. Open Universe (k=-1,40 1/2) 8.4.1. Radiation-dominated Universe (perfect-fluid approximation) 8.4.2. Matter-dominated Universe (dust approximation) Big Bang: a radiation/matter-dominated singularity 100 101 105 105 106 107 9. Cosmological constant and the dark Universe 111 9.1. Age of a matter-dominated Friedmann Universe 111 9.2. Einstein's field equations revisited: cosmological constant 112 9.3. Age of the Universe revisited 115 9.4. Particle horizon revisited: the horizon problem 116 9.5. Possible solutions to the horizon problem 9.5.1. Inflation 117 117 10. Cosmic distances 123 10.1. Redshift 123 10.2. Proper distance 124 10.3. Comoving coordinates and comoving distance 124 10.4. Angular diameter distance 126 10.5. Luminosity distance 127 10.6. Particle horizon 128 11. Summary of the foundations of cosmology 133 11.1. General relativity: kinematics in curved spacetime 133 11.2. Cosmology: solutions of Friedmann's equations 135 11.3. Expanding Universe 136 12. Cosmic content 139
12.1. Particle distribution function 139 12.2. Particle distributionfunction of species 141 12.3. Entropy density 142 ix
X Contents 12.4. Cosmic microwave background photons 143 12.5. Cosmic neutrino background 144 12.6. Baryonic matter 148 12.7. Dark matter 148 150 12.7.1. Evidence for dark matter: rotation curves in disk galaxies 12.7.2. Other evidence for dark matter 12.7.3. Dark-matter candidates 12.8. Dark energy 151 152 156 12.8.1. Detecting dark energy using luminosity distance vs. redshift 12.8.2. Investigating other forms of dark energy 158 12.8.3. Alternative to dark energy 162 13. Brief history of the early Universe 165 161 13.1. Keeping track of the Universe's history 165 13.2. Early Universe at a glance: major benchmarks 166 13.3. Very early Universe: the first three minutes 167 167 13.3.1. The Big Bang: t = 0 s 13.3.2. The Planck epoch: 0 t 10-43 s 13.3.3. 13.3.4. 13.3.5. 13.3.6. 13.3.7. Grand unification epoch: 10~43 s t 10~36 s Inflationary epoch: 10-36 s t IO-32 s Electroweak epoch: 10-32 s t 10“12 s Quark epoch: 10-12 s t 10-6 s Hadron epoch: 10“6 s t 1 s 13.3.8. Lepton epoch: 1 s t 3 min 13.4. Early Universe: the first 400,000 years 13.4.1. The earliest Universe: T 1012 К 13.4.2. Neutrino decoupling: T «3 x 1010K 13.4.3. Neutron:proton ratio freezes out: T « 1010 К 13.4.4. Electron-positron annihilation: T~3x 109K 13.4.5. The epoch of nucleosynthesis: 109K T 3xl0sK 168 169 169 170 170 171 171 173 173 174 175 176 176 13.4.6. Transition from radiation-dominated Universe to matter-dominated Universe: Т^Ю, 000 К 13.4.7. Recombination: T «4000 К 176 177 14. Cosmic microwave background radiation 181 14.1. Importance of the CMB radiation 14.1.1. Blackbody spectrum 14.1.2. Number
density ofthe CMBphotons 181 182 183 14.2. Systematic bias: the dipole anisotropy 14.2.1. Relativistic Doppler shift 184 185 14.3. Angular power spectrum 14.3.1. Two-point correlation function vs. angular power spectrum 14.3.2. Cosmic variance 187 189 189
Contents 14.4. Seales in the angular power spectrum 190 14.5. Baryon acoustic oscillations 14.5.1. Dampening of the overtones 190 192 14.6. Physical effects affecting the CMB radiation 193 14.6.1. Sunyaev-Zel’dovich effect 14.6.2. Sachs-Wolfe effect 14.6.3. Integrated Sachs-Wolfe effect 193 193 194 Epilogue 197 Further reading 199 A. An alternative Lagrangian 201 B. Geodesic equation in spherical coordinates 203 C. Example of metric conversion 207 D. Applying the geodesic equation 209 E. Matter-dark energy equality 211 F. Radiation-dark energy equality 213 G. Radiation-matter equality 215 H. Chemical potential 217 I. How to compute the relative abundancesof the light elements 219 J. Equation of state for the perfect fluid 223 K. Origins of the large-scale structure in theUniverse 225 Constants, units, and conversions 231 References 233 Index 237 xi |
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| spelling | Terzić, Balša Verfasser aut Relativity and cosmology from first principles to interpretations Balša Terzić, Old Dominion University, Norfolk, VA, USA London ; San Diego ; Cambridge Academic Press [2025] xvi, 239 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Kosmologie (DE-588)4114294-9 gnd rswk-swf Gravitation (DE-588)4021908-2 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Kosmologie (DE-588)4114294-9 s Relativitätstheorie (DE-588)4049363-5 s Gravitation (DE-588)4021908-2 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035209420&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Terzić, Balša Relativity and cosmology from first principles to interpretations Kosmologie (DE-588)4114294-9 gnd Gravitation (DE-588)4021908-2 gnd Relativitätstheorie (DE-588)4049363-5 gnd |
| subject_GND | (DE-588)4114294-9 (DE-588)4021908-2 (DE-588)4049363-5 |
| title | Relativity and cosmology from first principles to interpretations |
| title_auth | Relativity and cosmology from first principles to interpretations |
| title_exact_search | Relativity and cosmology from first principles to interpretations |
| title_full | Relativity and cosmology from first principles to interpretations Balša Terzić, Old Dominion University, Norfolk, VA, USA |
| title_fullStr | Relativity and cosmology from first principles to interpretations Balša Terzić, Old Dominion University, Norfolk, VA, USA |
| title_full_unstemmed | Relativity and cosmology from first principles to interpretations Balša Terzić, Old Dominion University, Norfolk, VA, USA |
| title_short | Relativity and cosmology |
| title_sort | relativity and cosmology from first principles to interpretations |
| title_sub | from first principles to interpretations |
| topic | Kosmologie (DE-588)4114294-9 gnd Gravitation (DE-588)4021908-2 gnd Relativitätstheorie (DE-588)4049363-5 gnd |
| topic_facet | Kosmologie Gravitation Relativitätstheorie |
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