| Foreword |
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ix | |
| Notation |
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xi | |
| Preface |
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xv | |
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1 | (50) |
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1.1 Is General Relativity the Final Theory of Gravity? |
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1 | (2) |
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1.2 What a Good Theory of Gravity Has to Do |
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3 | (11) |
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1.2.1 The Foundation of Metric Theories: The Equivalence Principle |
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7 | (2) |
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1.2.2 The Parametrized Post Newtonian (PPN) Limit |
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9 | (1) |
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1.2.3 Mach's Principle and G Variability |
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10 | (4) |
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1.2.4 Gravity at High and Low Energies |
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14 | (1) |
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1.3 The Problem of Quantum Gravity |
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14 | (11) |
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1.3.1 Intrinsic Limits in General Relativity and Quantum Field Theory |
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14 | (1) |
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1.3.2 The Perturbative Covariant Approach and the Canonical Approach |
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15 | (4) |
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1.3.3 A Conceptual Clash: Disagreement between the Approaches |
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19 | (1) |
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1.3.4 Matching General Relativity with Quantum Fields: The Semiclassical Limit Approach |
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20 | (3) |
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1.3.5 Induced Gravity and Emergent Gravity |
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23 | (1) |
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1.3.6 Towards Quantum Gravity |
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24 | (1) |
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1.4 Cosmological and Astrophysical Riddles |
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25 | (23) |
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1.4.1 The First Need for Acceleration |
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28 | (2) |
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1.4.2 Observations, Precision Cosmology and Cosmological Constant |
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30 | (7) |
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1.4.3 Scalar Fields in Early Universe |
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37 | (2) |
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1.4.4 Inflationary Models |
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39 | (5) |
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1.4.5 The Dark Energy Problem |
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44 | (3) |
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1.4.6 The Dark Matter Problem |
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47 | (1) |
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1.5 The Status of Gravity |
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48 | (3) |
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2 Gravity Emerging from Poincare Gauge Invariance |
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51 | (52) |
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2.1 General Considerations on the Gauge Theories |
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51 | (3) |
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2.2 The Bundle Approach to the Gauge Theories |
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54 | (5) |
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59 | (2) |
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2.4 The Conformal-Affine Lie Algebra |
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61 | (1) |
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2.5 Group Actions and Bundle Morphisms |
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62 | (1) |
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2.6 Nonlinear Realizations and Generalized Gauge Transformations |
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63 | (2) |
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2.7 The Covariant Coset Field Transformations |
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65 | (1) |
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2.8 The Decomposition of Connections in πPM: P → M |
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66 | (8) |
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2.8.1 Conformal-Affine Nonlinear Gauge Potential in πPM: P → M |
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68 | (1) |
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2.8.2 Conformal-Affine Nonlinear Gauge Potential in π P Σ: P → Σ |
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69 | (1) |
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2.8.3 Conformal-Affine Nonlinear Gauge Potential on ΠΣM: Σ → M |
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69 | (5) |
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74 | (1) |
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2.10 The Cartan Structure Equations |
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74 | (1) |
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2.11 The Bianchi Identities |
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75 | (2) |
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2.12 The Action Functional and the Gauge Field Equations |
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77 | (3) |
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2.13 Invariance Principles |
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80 | (3) |
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2.14 Global Poincare Invariance |
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83 | (1) |
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2.15 Local Poincare Invariance |
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84 | (3) |
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2.16 Spinors, Vectors and Tetrads |
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87 | (6) |
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2.17 Curvature, Torsion and Metric |
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93 | (3) |
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2.18 The Field Equations of Gravity |
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96 | (7) |
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3 Space-Time Deformations |
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103 | (10) |
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3.1 Deformations and Conformal Transformations |
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103 | (1) |
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3.2 Generalities in Space-Time Deformations |
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104 | (1) |
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3.3 Properties of Deforming Matrices |
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105 | (3) |
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3.4 Metric Deformations as Perturbations |
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108 | (2) |
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3.5 Approximate Killing Vectors |
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110 | (3) |
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4 Extended Theories of Gravity |
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113 | (26) |
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4.1 The Effective Action and the Field Equations |
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117 | (3) |
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4.2 Conformal Transformations |
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120 | (2) |
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4.3 The Intrinsic Conformal Structure |
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122 | (6) |
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4.4 Cosmological Solutions in the Einstein and Jordan Frames |
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128 | (9) |
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4.4.1 Some Relevant Examples |
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133 | (4) |
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137 | (2) |
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5 Probing the Post-Minkowskian Limit |
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139 | (26) |
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5.1 Gravitational Waves in Extended Gravity |
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139 | (1) |
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5.2 The Post Minkowskian Limit of Extended Gravity: The Case of f(R)-Gravity |
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140 | (3) |
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5.3 The General Theory: Ghost, Massless and Massive Modes |
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143 | (5) |
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5.4 Polarization States of Gravitational Waves |
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148 | (2) |
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5.5 Potential Detection by Interferometers |
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150 | (2) |
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5.6 The Stochastic Background of Gravitational Waves |
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152 | (6) |
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5.7 The Gravitational Stochastic Background "Tuned" by Extended Gravity |
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158 | (7) |
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6 Probing the Post Newtonian Limit |
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165 | (40) |
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6.1 The Problem of Newtonian Limit in Extended Gravity |
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165 | (1) |
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6.2 The Field Equations and the Newtonian Limit |
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166 | (3) |
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6.2.1 General Form of the Field Equations |
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166 | (1) |
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6.2.2 The Newtonian Limit |
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167 | (1) |
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6.2.3 The Quadratic Lagrangians and the Newtonian Limit of the Field Equations |
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168 | (1) |
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6.2.4 The Combined Lagrangian |
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169 | (1) |
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6.3 Considerations on the Field Equations in the Newtonian Limit |
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169 | (4) |
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6.3.1 The General Approach to Decouple the Field Equations |
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170 | (1) |
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6.3.2 Green Functions for Particular Values of the Coupling Constants |
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171 | (2) |
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6.4 Solutions by the Green Functions |
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173 | (1) |
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6.4.1 Field Equations for Particular Values of the Coupling Constants |
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173 | (1) |
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6.5 Green's Functions for Spherically Symmetric Systems |
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174 | (4) |
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6.5.1 A General Green Function for the Decoupled Field Equations |
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174 | (4) |
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6.6 Fourth Order Gravity and Experimental Constraints on Eddington Parameters |
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178 | (3) |
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6.7 Fourth Order Theories Compatible with Experimental Limits on γ and β |
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181 | (1) |
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6.8 Comparing with Experimental Measurements |
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182 | (2) |
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184 | (12) |
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6.10 Constraining f(R)-models by PPN Parameters |
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196 | (4) |
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6.11 Further Experimental Constrainsts |
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200 | (5) |
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7 Future Perspectives and Conclusions |
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205 | (6) |
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205 | (4) |
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209 | (2) |
| References |
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211 | (20) |
| Index |
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231 | |
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