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Tables of Contents for An Introduction to Mathematical Cosmology
Preface to the first edition
ix
Preface to the second edition
xi
Some basic concepts and an overview of cosmology
1
11
Introduction to general relativity
12
25
Summary of general relativity
12
6
Some special topics in general relativity
18
19
Killing vectors18
3
Tensor densities21
3
Gauss and Stokes theorems24
4
The action principle for gravitation28
4
Some further topics32
5
The Robertson-Walker metric
37
23
A simple derivation of the Robertson-Walker metric
37
5
Some geometric properties of the Robertson-Walker metric
42
3
Some kinematic properties of the Robertson-Walker metric
45
6
The Einstein equations for the Robertson-Walker metric
51
2
Rigorous derivation of the Robertson-Walker metric
53
7
Exact solution for zero pressure
64
3
Solution for pure radiation
67
1
Exact solution connecting radiation and matter eras
68
3
The red-shift versus distance relation
71
2
Particle and event horizons
73
3
The Hubble constant and the deceleration parameter
76
18
Further remarks about observational cosmology
85
9
Appendix to Chapter 590
4
Models with a cosmological constant
94
18
Further remarks about the cosmological constant
98
2
Limits on the cosmological constant
100
2
Some recent developments regarding the cosmological constant and related matters
102
10
Introduction102
2
An exact solution with cosmological constant104
3
Restriction of parameter space107
5
Singularities in cosmology
112
16
Homogeneous cosmologies
113
2
Some results of general relativistic hydrodynamics
115
3
Definition of singularities
118
2
An example of a singularity theorem
120
1
The oscillatory approach to singularities
122
4
A singularity-free universe?
126
2
The very early universe
135
7
Equations in the early universe
142
1
Black-body radiation and the temperature of the early universe
143
5
Evolution of the mass-energy density
148
5
Nucleosynthesis in the early universe
153
6
Further remarks about helium and deuterium
159
5
Neutrino types and masses
164
2
The very early universe and inflation
166
23
Inflationary models - qualitative discussion
167
7
Inflationary models - quantitative description
174
4
An exact inflationary solution
178
2
Further remarks on inflation
180
3
More inflationary solutions
183
6
Appendix to Chapter 9186
3
Hamiltonian formalism
191
4
The Schrodinger functional equation for a scalar field
195
2
A functional differential equation
197
2
Solution for a scalar field
199
1
The free electromagnetic field
199
2
The Wheeler-De Witt equation
201
1
Conformal fluctuations
206
3
Further remarks about quantum cosmology
209
2
The distant future of the universe
211
9
Three ways for a star to die
211
2
Galactic and supergalactic black holes
213
2
Black-hole evaporation
215
1
Slow and subtle changes
216
2
A collapsing universe
218
2
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