Part IV Cosmology
12 The Einstein Field Equations for Cosmology . . . . . . . . . . . . . . . . . 193
12.1 The Field Equations and Energy-Momentum Conservation . . . . 193
12.2 Field Equations and the Cosmic Fluid Source . . . . . . . . . . . . . . 195
12.3 The Cosmological Constant as Vacuum or Dark Energy . . . . . . 198
12.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
13 Cosmological Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
13.1 Basic Observations and Assumptions . . . . . . . . . . . . . . . . . . . . 203
13.2 The Cosmological FLRW Metric . . . . . . . . . . . . . . . . . . . . . . . 207
13.3 Consequences of the Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
13.4 De Sitter Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
14 The Dynamical Equations of Cosmology . . . . . . . . . . . . . . . . . . . . . 223
14.1 The Einstein Field Equations for Cosmology . . . . . . . . . . . . . . 223
14.2 Critical Density and the Shape of the Universe . . . . . . . . . . . . . 225
14.3 Observed Dark Matter and Dark Energy Densities . . . . . . . . . . 226
14.4 Evolution of Cosmic Fluid Constituents . . . . . . . . . . . . . . . . . . 227
14.5 The Friedmann Master Equation . . . . . . . . . . . . . . . . . . . . . . . 230
15 Solutions for the Present Universe . . . . . . . . . . . . . . . . . . . . . . . . . 233
15.1 The Positive Cosmological Constant . . . . . . . . . . . . . . . . . . . . 233
15.2 Complete Solution of the Friedmann Master Equation . . . . . . . . 234
15.3 Cosmological Constant Dominance . . . . . . . . . . . . . . . . . . . . . 234
15.4 Matter Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
15.5 The LCDM Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
16 Some Properties of the LCDM Universe . . . . . . . . . . . . . . . . . . . . . 247
16.1 Diverse Cosmological Observations . . . . . . . . . . . . . . . . . . . . . 247
16.2 Cosmological Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . 251
16.3 The Hubble Function and the Age of the Universe . . . . . . . . . . 252
16.4 Transition Time for Matter to Dark Energy Dominance . . . . . . . 253
16.5 Density Ratios and the Shape of the Universe . . . . . . . . . . . . . 254
16.6 Horizons and the Size of the Observable Universe . . . . . . . . . . 257
16.7 Conformal Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
17 Earlier Times and Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
17.1 Radiation and Temperature in Earlier Times . . . . . . . . . . . . . . . 263
17.2 The Scale Factor and Basic Properties of the Radiation Era . . . . 267
17.3 The Isotropic CMB and the Horizon Puzzle . . . . . . . . . . . . . . . 269
17.4 The Anisotropies of the CMB . . . . . . . . . . . . . . . . . . . . . . . . . 270
18 A Brief Historical Overview of the Universe . . . . . . . . . . . . . . . . . . 275
18.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
18.2 Condensation of Stars and Galaxies . . . . . . . . . . . . . . . . . . . . . 277
18.3 Condensation of Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Contents
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12 The Einstein Field Equations for Cosmology . . . . . . . . . . . . . . . . . 193
12.1 The Field Equations and Energy-Momentum Conservation . . . . 193
12.2 Field Equations and the Cosmic Fluid Source . . . . . . . . . . . . . . 195
12.3 The Cosmological Constant as Vacuum or Dark Energy . . . . . . 198
12.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
13 Cosmological Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
13.1 Basic Observations and Assumptions . . . . . . . . . . . . . . . . . . . . 203
13.2 The Cosmological FLRW Metric . . . . . . . . . . . . . . . . . . . . . . . 207
13.3 Consequences of the Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
13.4 De Sitter Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
14 The Dynamical Equations of Cosmology . . . . . . . . . . . . . . . . . . . . . 223
14.1 The Einstein Field Equations for Cosmology . . . . . . . . . . . . . . 223
14.2 Critical Density and the Shape of the Universe . . . . . . . . . . . . . 225
14.3 Observed Dark Matter and Dark Energy Densities . . . . . . . . . . 226
14.4 Evolution of Cosmic Fluid Constituents . . . . . . . . . . . . . . . . . . 227
14.5 The Friedmann Master Equation . . . . . . . . . . . . . . . . . . . . . . . 230
15 Solutions for the Present Universe . . . . . . . . . . . . . . . . . . . . . . . . . 233
15.1 The Positive Cosmological Constant . . . . . . . . . . . . . . . . . . . . 233
15.2 Complete Solution of the Friedmann Master Equation . . . . . . . . 234
15.3 Cosmological Constant Dominance . . . . . . . . . . . . . . . . . . . . . 234
15.4 Matter Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
15.5 The LCDM Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
16 Some Properties of the LCDM Universe . . . . . . . . . . . . . . . . . . . . . 247
16.1 Diverse Cosmological Observations . . . . . . . . . . . . . . . . . . . . . 247
16.2 Cosmological Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . 251
16.3 The Hubble Function and the Age of the Universe . . . . . . . . . . 252
16.4 Transition Time for Matter to Dark Energy Dominance . . . . . . . 253
16.5 Density Ratios and the Shape of the Universe . . . . . . . . . . . . . 254
16.6 Horizons and the Size of the Observable Universe . . . . . . . . . . 257
16.7 Conformal Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
17 Earlier Times and Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
17.1 Radiation and Temperature in Earlier Times . . . . . . . . . . . . . . . 263
17.2 The Scale Factor and Basic Properties of the Radiation Era . . . . 267
17.3 The Isotropic CMB and the Horizon Puzzle . . . . . . . . . . . . . . . 269
17.4 The Anisotropies of the CMB . . . . . . . . . . . . . . . . . . . . . . . . . 270
18 A Brief Historical Overview of the Universe . . . . . . . . . . . . . . . . . . 275
18.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
18.2 Condensation of Stars and Galaxies . . . . . . . . . . . . . . . . . . . . . 277
18.3 Condensation of Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Contents
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