The dynamics of inhomogeneous cosmologies

Background in cosmology......Page 11
Cosmological Hierarchy......Page 14
Goals......Page 18
Overview......Page 20
I Dynamics of G2 and SH cosmologies......Page 22
1+3 decomposition......Page 23
1+1+2 decomposition for G2 cosmologies......Page 29
Scale-invariant variables......Page 33
The G2 hierarchy......Page 39
G2-compatible SH cosmologies......Page 43
The standard Mixmaster dynamics......Page 50
The G2-compatible SH evolution equations......Page 56
Generalized Mixmaster dynamics......Page 61
Non-Mixmaster dynamics......Page 75
Future asymptotics......Page 78
The evolution equations......Page 83
Invariant subsets of the -normalized state space......Page 90
Asymptotic silence......Page 95
An explicit solution with ``steps\"......Page 101
An explicit solution with ``spikes\"......Page 106
Spiky and step-like structures......Page 114
Dynamics in the past asymptotic regime......Page 116
Background dynamics: role of algebraic terms......Page 117
Effects of spatial inhomogeneity I: role of saddles......Page 119
Effects of spatial inhomogeneity II: role of spatial derivative terms......Page 125
II Numerical exploration of G2 cosmologies......Page 127
Equations for numerical simulations......Page 128
Specifying the initial conditions......Page 129
Is the system hyperbolic?......Page 133
Accuracy of numerical schemes......Page 134
Unsatisfactory aspects of the numerical simulations......Page 141
Numerical simulations......Page 143
Local Mixmaster dynamics......Page 144
Spatial variation in the background dynamics......Page 149
Multiple transitions......Page 151
Step-like structures......Page 153
Spiky structures......Page 158
Spike transitions......Page 161
Shock waves......Page 167
Future asymptotics......Page 171
Close-to-FL epoch......Page 173
Conclusion......Page 182
G2 action......Page 185
Rotation formulae......Page 190
Asymptotic expansions at spike points......Page 192
Equations for numerical simulations......Page 195
Bibliography......Page 198