Preface |
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xi | |
Part 1 Foundations |
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1 The nature of cosmology |
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3 | (22) |
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1.1 The aims of cosmology |
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3 | (2) |
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1.2 Observational evidence and its limitations |
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5 | (4) |
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1.3 A summary of current observations |
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9 | (8) |
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1.4 Cosmological concepts |
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17 | (3) |
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20 | (3) |
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23 | (2) |
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25 | (31) |
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26 | (2) |
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2.2 Tangent vectors and 1-forms |
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28 | (3) |
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31 | (3) |
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34 | (1) |
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2.5 Connections and covariant derivatives |
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35 | (2) |
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37 | (2) |
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39 | (12) |
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2.8 General bases and tetrads |
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51 | (2) |
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53 | (3) |
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3 Classical physics and gravity |
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56 | (17) |
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3.1 Equivalence principles, gravity and local physics |
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56 | (5) |
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3.2 Conservation equations |
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61 | (3) |
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3.3 The field equations in relativity and their structure |
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64 | (5) |
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3.4 Relation to Newtonian theory |
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69 | (4) |
Part 2 Relativistic cosmological models |
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4 Kinematics of cosmological models |
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73 | (16) |
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73 | (1) |
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4.2 The fundamental 4-velocity |
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74 | (1) |
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4.3 Time derivatives and the acceleration vector |
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75 | (1) |
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4.4 Projection to give three-dimensional relations |
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76 | (3) |
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4.5 Relative position and velocity |
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79 | (1) |
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4.6 The kinematic quantities |
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80 | (6) |
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4.7 Curvature and the Ricci identities for the 4-velocity |
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86 | (2) |
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4.8 Identities for the projected covariant derivatives |
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88 | (1) |
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89 | (30) |
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90 | (5) |
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95 | (6) |
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101 | (3) |
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104 | (6) |
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5.5 Electromagnetic fields |
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110 | (5) |
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115 | (2) |
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117 | (2) |
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6 Dynamics of cosmological models |
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119 | (34) |
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6.1 The Raychaudhuri-Ehlers equation |
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119 | (5) |
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6.2 Vorticity conservation |
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124 | (2) |
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6.3 The other Einstein field equations |
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126 | (6) |
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6.4 The Weyl tensor and the Bianchi identities |
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132 | (2) |
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6.5 The orthonormal 1+3 tetrad equations |
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134 | (5) |
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6.6 Structure of the 1+3 system of equations |
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139 | (4) |
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6.7 Global structure and singularities |
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143 | (4) |
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6.8 Newtonian models and Newtonian limits |
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147 | (6) |
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7 Observations in cosmological models |
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153 | (27) |
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7.1 Geometrical optics and null geodesics |
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153 | (3) |
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156 | (3) |
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7.3 Geometry of null geodesics and images |
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159 | (2) |
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7.4 Radiation energy and flux |
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161 | (6) |
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7.5 Specific intensity and apparent brightness |
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167 | (3) |
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170 | (1) |
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7.7 Selection and detection issues |
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171 | (1) |
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172 | (1) |
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7.9 Causal and visual horizons |
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173 | (7) |
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8 Light-cone approach to relativistic cosmology |
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180 | (21) |
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180 | (1) |
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8.2 Direct observational cosmology |
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181 | (5) |
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186 | (1) |
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8.4 Field equations: determining the geometry |
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187 | (3) |
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8.5 Isotropic and partially isotropic observations |
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190 | (4) |
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8.6 Implications and opportunities |
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194 | (7) |
Part 3 The standard model and extensions |
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9 Homogeneous FLRW universes |
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201 | (48) |
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202 | (8) |
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210 | (2) |
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9.3 FLRW dynamics with barotropic fluids |
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212 | (8) |
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220 | (5) |
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225 | (1) |
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9.6 Thermal history and contents of the universe |
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226 | (12) |
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238 | (8) |
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9.8 Origin of FLRW geometry |
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246 | (1) |
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247 | (2) |
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10 Perturbations of FLRW universes |
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249 | (33) |
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10.1 The gauge problem in cosmology |
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250 | (1) |
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10.2 Metric-based perturbation theory |
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251 | (11) |
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10.3 Covariant nonlinear perturbations |
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262 | (5) |
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10.4 Covariant linear perturbations |
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267 | (15) |
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11 The cosmic background radiation |
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282 | (25) |
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11.1 The CMB and spatial homogeneity: nonlinear analysis |
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282 | (5) |
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11.2 Linearized analysis of distribution multipoles |
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287 | (5) |
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11.3 Temperature anisotropies in the CMB |
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292 | (2) |
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294 | (1) |
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11.5 Scalar perturbations |
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295 | (5) |
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300 | (3) |
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11.7 Vector and tensor perturbations |
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303 | (1) |
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11.8 Other background radiation |
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303 | (4) |
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12 Structure formation and gravitational lensing |
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307 | (38) |
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12.1 Correlation functions and power spectra |
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307 | (2) |
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12.2 Primordial perturbations from inflation |
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309 | (8) |
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12.3 Growth of density perturbations |
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317 | (13) |
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12.4 Gravitational lensing |
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330 | (9) |
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12.5 Cosmological applications of lensing |
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339 | (6) |
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13 Confronting the Standard Model with observations |
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345 | (25) |
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13.1 Observational basis for FLRW models |
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346 | (5) |
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13.2 FLRW observations: probing the background evolution |
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351 | (4) |
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13.3 Almost FLRW observations: probing structure formation |
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355 | (8) |
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13.4 Constraints and consistency checks |
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363 | (3) |
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13.5 Concordance model and further issues |
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366 | (4) |
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14 Acceleration from dark energy or modified gravity |
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370 | (25) |
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14.1 Overview of the problem |
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370 | (3) |
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14.2 Dark energy in an FLRW background |
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373 | (3) |
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14.3 Modified gravity in a RW background |
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376 | (14) |
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14.4 Constraining effective theories |
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390 | (1) |
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391 | (4) |
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15 'Acceleration' from large-scale inhomogeneity? |
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395 | (21) |
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15.1 Lemaitre-Tolman-Bondi universes |
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395 | (4) |
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15.2 Observables and source evolution |
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399 | (2) |
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15.3 Can we fit area distance and number count observations? |
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401 | (2) |
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15.4 Testing background LTB with SNIa and CMB distances |
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403 | (3) |
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15.5 Perturbations of LTB |
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406 | (5) |
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15.6 Observational tests of spatial homogeneity |
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411 | (4) |
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15.7 Conclusion: status of the Copernican Principle |
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415 | (1) |
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16 'Acceleration' from small-scale inhomogeneity? |
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416 | (31) |
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16.1 Different scale descriptions |
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416 | (5) |
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16.2 Cosmological backreaction |
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421 | (2) |
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16.3 Specific models: almost FLRW |
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423 | (3) |
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16.4 Inhomogeneous models |
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426 | (6) |
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16.5 Importance of backreaction effects? |
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432 | (3) |
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16.6 Effects on observations |
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435 | (5) |
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16.7 Combination of effects: altering cosmic concordance? |
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440 | (1) |
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16.8 Entropy and coarse-graining |
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441 | (6) |
Part 4 Anisotropic and inhomogeneous models |
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17 The space of cosmological models |
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447 | (9) |
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17.1 Cosmological models with symmetries |
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447 | (5) |
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17.2 The equivalence problem in cosmology |
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452 | (1) |
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17.3 The space of models and the role of symmetric models |
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453 | (3) |
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18 Spatially homogeneous anisotropic models |
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456 | (32) |
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18.1 Kantowski-Sachs universes: geometry and dynamics |
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457 | (1) |
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18.2 Bianchi I universes: geometry and dynamics |
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458 | (4) |
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18.3 Bianchi geometries and their field equations |
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462 | (5) |
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18.4 Bianchi universe dynamics |
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467 | (7) |
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18.5 Evolution of particular Bianchi models |
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474 | (7) |
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18.6 Cosmological consequences |
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481 | (5) |
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18.7 The Bianchi degrees of freedom |
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486 | (2) |
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488 | (23) |
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490 | (1) |
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19.2 Swiss cheese revisited |
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491 | (2) |
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493 | (2) |
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19.4 Models with a G3 acting on S2 |
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495 | (1) |
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496 | (2) |
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19.6 The Szekeres-Szafron family |
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498 | (3) |
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19.7 The Stephani-Barnes family |
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501 | (1) |
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501 | (1) |
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19.9 General dynamics of inhomogeneous models |
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502 | (1) |
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19.10 Cosmological applications |
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503 | (8) |
Part 5 Broader perspectives |
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20 Quantum gravity and the start of the universe |
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511 | (24) |
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20.1 Is there a quantum gravity epoch? |
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511 | (1) |
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20.2 Quantum gravity effects |
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512 | (4) |
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20.3 String theory and cosmology |
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516 | (10) |
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20.4 Loop quantum gravity and cosmology |
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526 | (4) |
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530 | (2) |
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20.6 Explaining the universe - the question of origins |
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532 | (3) |
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21 Cosmology in a larger setting |
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535 | (20) |
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21.1 Local physics and cosmology |
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535 | (4) |
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539 | (3) |
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21.3 Anthropic question: fine-tuning for life |
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542 | (4) |
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21.4 Special or general? Probable or improbable? |
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546 | (2) |
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21.5 Possible existence of multiverses |
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548 | (6) |
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21.6 Why is the universe as it is? |
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554 | (1) |
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22 Conclusion: our picture of the universe |
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555 | (6) |
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555 | (3) |
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22.2 Testing alternatives: probing the possibilities |
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558 | (1) |
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559 | (2) |
Appendix Some useful formulae |
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561 | (5) |
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561 | (2) |
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A.2 1+3 covariant equations |
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563 | (2) |
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A.3 Frequently used acronyms |
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565 | (1) |
References |
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566 | (40) |
Index |
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606 | |