| Preface | p. V |
| Introduction | p. 1 |
| Remarks on cosmological special relativity | p. 1 |
| Cosmological Special Relativity | p. 3 |
| The Galileo transformation and its generalization | p. 3 |
| The Galileo transformation | p. 3 |
| Difficulties with light | p. 5 |
| Role of velocity in classical physics | p. 5 |
| Nonrelativistic cosmological transformation | p. 6 |
| Nonrelativistic transformation | p. 6 |
| Difficulties at the Big Bang | p. 6 |
| Extension to the Lorentz transformation | p. 8 |
| Invariance of light propagation | p. 8 |
| The Lorentz transformation | p. 8 |
| Extension to the cosmological transformation | p. 9 |
| Invariance of the Big Bang time | p. 9 |
| The cosmological transformation | p. 9 |
| Temperature of the Universe | p. 10 |
| Conclusions | p. 11 |
| Line elements in Einstein's special relativity and in cosmological special relativity | p. 11 |
| Line element in Einstein's relativity | p. 11 |
| Light propagation | p. 12 |
| Line element in cosmological special relativity | p. 12 |
| Hubble's expansion | p. 12 |
| Inflation of the Universe | p. 15 |
| Matter density | p. 15 |
| Ratio of volumes | p. 16 |
| Minimal acceleration in Nature | p. 16 |
| Relation to Pioneer spacecrafts | p. 17 |
| Redshift and cosmic time | p. 17 |
| Field equations of a different kind | p. 19 |
| Examples | p. 21 |
| Cosmological special relativity in five dimensions | p. 22 |
| Subtransformations | p. 23 |
| Electrodynamics in five dimensions | p. 24 |
| Field equations | p. 25 |
| Generalized Maxwell's equations | p. 25 |
| The mix-up | p. 26 |
| Does the Cabibbo angle describe a rotation in the time-velocity plane? | p. 28 |
| Elements of General Relativity | p. 29 |
| Riemannian geometry | p. 29 |
| Transformation of coordinates | p. 29 |
| Contravariant vectors | p. 30 |
| Invariants. Covariant vectors | p. 31 |
| Tensors | p. 32 |
| Metric tensor | p. 32 |
| Christoffel symbols | p. 33 |
| Covariant differentiation | p. 34 |
| Riemann, Ricci and Einstein tensors | p. 36 |
| Geodesics | p. 37 |
| Bianchi identities | p. 38 |
| Principle of equivalence | p. 39 |
| Null experiments. Eotvos experiment | p. 39 |
| Principle of general covariance | p. 41 |
| Gravitational field equations | p. 42 |
| Einstein's field equations | p. 43 |
| Deduction of Einstein's equations from variational principle | p. 44 |
| The electromagnetic energy-momentum tensor | p. 45 |
| The Schwarzschild metric | p. 46 |
| Experimental tests of general relativity | p. 51 |
| Gravitational red shift | p. 51 |
| Effects on planetary motion | p. 52 |
| Deflection of light | p. 56 |
| Gravitational radiation experiments | p. 59 |
| Radar experiment | p. 59 |
| Low-temperature experiments | p. 60 |
| Equations of motion | p. 61 |
| Geodesic postulate | p. 61 |
| Equations of motion as a consequence of field equations | p. 61 |
| Self-action terms | p. 63 |
| Einstein-Infeld-Hoffmann method | p. 67 |
| Newtonian equation of motion | p. 69 |
| Einstein-Infeld-Hoffmann equation | p. 70 |
| Decomposition of the Riemann tensor | p. 71 |
| Cosmological General Relativity | p. 73 |
| Introduction | p. 73 |
| Space and velocity | p. 74 |
| Gravitational field equations | p. 74 |
| Universe expansion | p. 75 |
| Energy-momentum tensor | p. 75 |
| Independent field equations | p. 76 |
| Solution of the field equations | p. 76 |
| Simple solution | p. 76 |
| Pressure | p. 77 |
| Line element | p. 77 |
| Physical meaning | p. 77 |
| [Omega subscript m] > 1 | p. 78 |
| [Omega subscript m] < 1 | p. 78 |
| [Omega subscript m] = 1 | p. 78 |
| The accelerating Universe | p. 78 |
| Tri-phase expansion | p. 79 |
| Theory versus experiment | p. 80 |
| Value of the Big Bang time [tau] | p. 80 |
| Value of [Characters not reproducible] | p. 82 |
| Comparison with general relativity | p. 84 |
| Recent developments on dark matter | p. 84 |
| Cosmological General Relativity in Five Dimensions | p. 87 |
| Introduction | p. 87 |
| Five-dimensional manifold of space, time and velocity | p. 87 |
| Universe with gravitation | p. 88 |
| The Bianchi identities | p. 89 |
| The gravitational field equations | p. 89 |
| Velocity as an independent coordinate | p. 90 |
| Effective mass density in cosmology | p. 90 |
| The accelerating Universe | p. 91 |
| Preliminaries | p. 91 |
| Expanding Universe | p. 93 |
| Decelerating, constant and accelerating expansions | p. 95 |
| Accelerating Universe | p. 96 |
| The Tully-Fisher formula: Nonexistence of halo dark matter | p. 97 |
| The Geodesic Equation | p. 98 |
| Equations of motion | p. 99 |
| The Tully-Fisher law | p. 102 |
| Cosmological redshift analysis | p. 104 |
| The redshift formula | p. 104 |
| Particular cases | p. 105 |
| Conclusions | p. 106 |
| Verification of the classical general relativity tests | p. 106 |
| Comparison with general relativity | p. 106 |
| Gravitational redshift | p. 109 |
| Motion in a centrally symmetric gravitational field | p. 111 |
| Deflection of light in a gravitational field | p. 117 |
| Gravitational waves | p. 120 |
| Mathematical Conventions | p. 123 |
| Components of the Ricci tensor | p. 124 |
| Integration of the Universe Expansion Equation | p. 127 |
| Index | p. 129 |
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