Structures in the Universe by Exact Methods: Formation, Evolution, Interactions

Half-title......Page 3
Series-title......Page 4
Title......Page 7
Copyright......Page 8
Contents......Page 9
Foreword......Page 13
Acknowledgements......Page 16
1 The purpose of this book......Page 17
Part I Theoretical background......Page 25
2.1.1 Basic properties......Page 27
2.1.2 Origin conditions......Page 29
2.1.3 Shell crossings, maxima and minima......Page 30
2.1.4 L–T models of cosmic structures......Page 31
1. A reformulation of the evolution equations......Page 32
2. Part I: density to density evolution......Page 33
3. Part II: velocity to density evolution......Page 35
4. Part III: velocity to velocity evolution......Page 36
2.1.6 Additional methods of specifying models......Page 38
1. Models with a simultaneous bang time......Page 39
2. Models that become homogeneous at late times......Page 41
3. Models with a simultaneous crunch time......Page 42
5. Models with a simultaneous time of maximum expansion......Page 44
7. Models with a given velocity profile at late times......Page 46
8. Models with a given density profile at late times......Page 47
2.1.7 Defining a model by initial and final profiles with Λ > 0......Page 49
2.1.8 A unified new form of the L–T solution......Page 55
2.2 The Lemaître model......Page 57
2.3.1 Definition and metric......Page 58
2.3.2 General properties of the Szekeres solutions......Page 61
2.3.3 Properties of the quasi-spherical Szekeres solution......Page 63
The significance of epsilon......Page 64
Shell crossings......Page 66
The mass-dipole......Page 68
3.1.1 Central observer......Page 71
3.1.2 Off-centre observer. SC method......Page 72
3.1.3 Off-centre observer. AA method......Page 74
3.2 Apparent and event horizons in the L–T model......Page 76
3.2.1 Apparent horizons......Page 77
3.2.3 Locating the AH- during expansion in elliptic regions......Page 79
3.2.4 AH- near an origin in elliptic regions......Page 80
3.2.5 AH+ during collapse in elliptic regions......Page 81
3.2.7 Apparent horizons in parabolic regions......Page 82
Definition......Page 83
Description......Page 84
Location of the event horizon......Page 85
3.3 Null geodesics in the quasi-spherical Szekeres model......Page 90
3.3.1 Constant (x, y) geodesics......Page 91
3.3.2 The redshift formula for the axial geodesics......Page 95
3.4 Junction of null geodesics in the Szekeres Swiss-cheese model......Page 97
3.5 The apparent horizons in the Szekeres model......Page 99
Part II Applications of the models in cosmology......Page 105
4.1.1 Transforming scales in the background......Page 107
4.1.2 Initial density and velocity fiuctuations......Page 108
4.2 The galaxy plus black hole formation model......Page 109
4.2.1 A galaxy with a central black hole......Page 110
4.2.2 The black hole interior......Page 111
4.2.3 A collapsed body......Page 112
The final density profile......Page 113
The initial fluctuation......Page 116
4.2.6 Numerical evolution of the models......Page 117
4.3.1 The most realistic model......Page 121
4.3.2 Results of some other numerical experiments......Page 122
4.4.1 The algorithm......Page 125
4.4.2 Void formation......Page 129
4.4.3 Void evolution......Page 130
4.5 Impact of radiation on void formation......Page 132
2. The initial density perturbations......Page 134
4. The radiation perturbations......Page 135
4.5.2 Results......Page 136
Constraints on background models......Page 141
4.6.1 The algorithm......Page 142
4.6.2 Double structures......Page 144
4.6.3 Connection to the large-scale structure of the Universe......Page 150
5 The cosmological constant and coincidence problems......Page 153
5.1 Constraints on model parameters from the SN Ia data......Page 154
5.1.1 The Λ CDM cosmological model......Page 156
5.1.2 L–T models with zero cosmological constant......Page 158
5.1.3 Illustration: flat L–T (Λ = 0) models......Page 160
5.1.4 Apparent acceleration......Page 162
5.3 The direct method......Page 164
5.3.1 Fitting the observations......Page 165
5.3.2 Further constraints on inhomogeneous models from CMB data......Page 170
5.3.3 Alnes, Amarzguioui and Grøn\'s proposal......Page 172
Central observer......Page 173
Off-centre observer......Page 175
5.3.4 GBH model......Page 177
5.3.5 L–T Swiss-cheese models......Page 179
Brouzakis et al.’s model......Page 180
Marra et al.’s model......Page 183
5.3.6 Effect of inhomogeneous expansion......Page 186
5.3.7 Summary of direct method investigations......Page 188
5.4.1 The flat case......Page 190
5.4.2 A map from {E(r),DL (z),R0 (r)} to M(r)......Page 193
5.4.3 Expansion fitting......Page 195
5.4.4 Extracting the cosmic metric from observations......Page 197
6.2 Permanent solution......Page 200
6.3 The Delayed Big Bang (DBB) model......Page 202
7.1 Light propagation effects......Page 205
7.1.2 Model specification and evaluation......Page 206
7.1.3 Arrangement of the Swiss-cheese model......Page 209
7.1.4 The Rees–Sciama effect......Page 213
7.2 CMB dipole and quadrupole in the DBB model with an off-centre observer......Page 216
7.2.1 Definition of the temperature......Page 217
7.2.2 Integration of the null geodesics and determination of the dipole and quadrupole moments......Page 218
7.2.3 Results and discussion......Page 220
7.3 CMB anisotropies in the Alnes et al. model with an off-centre observer......Page 222
1. Evolution of galactic black holes......Page 225
2. Evolution of cosmic structures......Page 226
3. The horizon problem......Page 227
4. Cosmological observations in the inhomogeneous universe......Page 228
References......Page 233
Index......Page 244