Table of Contents
Preface xi
Acknowledgments xv
I Homogeneity and clustering 3
1 Homogeneity and clustering 3
2 Is the universe homogeneous? 3
3 Physical principles 11
4 How did galaxies and clusters of galaxies form? 18
5 Summary 35
II Behavior of irregularities in the distribution of matter: newtonian approximation 37
6 Newtonian approximation 37
7 Particle dynamics in expanding coordinates 41
8 The peculiar acceleration 43
9 Two models: the Vlasov equation and the ideal fluid 45
10 Linear perturbation approximation for δ 49
11 Solutions for δ(t): p = Λ = 0 51
12 Solutions for δ(t): effect of a uniform radiation background 56
13 Solutions for δ(t): models with Λ ≠ 0 59
14 The peculiar velocity field 63
15 Joining conditions for δ and υ 66
16 Critical Jeans length 68
17 Primeval magnetic field as a source for δρ/ρ 71
18 Second order perturbation theory for δρ/ρ 74
19 Spherical model 77
20 Homogeneous ellipsoid model 86
21 Caustics and pancakes 95
22 Expansion, vorticity, and shear 103
23 Origin of the rotation of galaxies 107
24 Cosmic energy equation 110
25 Spherical accretion model 115
26 Hierarchical clustering model 120
27 Fourier transform of the equations of motion 124
28 Coupling of density fluctuations 128
III n-Point correlation functions: descriptive statistics 138
29 Statistical measures of the galaxy distribution 138
30 Fair sample hypothesis 142
31 Two-point spatial correlation function ξ(r) 143
32 Two-point correlation function: another definition 145
33 Two-point correlation function: Poisson model 147
34 Three-point correlation function 148
35 Four-point correlation function 150
36 Moments of counts of objects 152
37 Constraints on ξ and ζ 156
38 Probability generating function 158
39 Estimates of PN 160
40 Cluster model 163
41 Power spectrum 166
42 Power law model for the spectrum 169
43 Bispectrum 171
44 Cross correlation function 172
45 Angular two-point correlation function 174
46 Angular power spectrum 175
47 Estimating w(θ) 183
48 Statistical uncertainty in the estimate of w(θ) 187
49 Relation between angular and spatial two-point correlation functions 189
50 Small separation approximation and the scaling relation 191
51 Decoupling of magnitude and position 194
52 Relation between ξ and w: some examples 195
53 Inversion of the equation 200
54 Angular three-point correlation function 203
55 Angular four-point correlation function 209
56 Correction for curvature and expansion 213
57 Summary of numerical results 221
58 Power spectrum of the extragalactic light 225
59 Moments of the number of neighbors 230
60 Model for PN 233
61 Clustering models 236
62 Continuous clustering hierarchy: Mandelbrot's prescription 243
63 The mass correlation functions 249
64 Clustering hierarchy: continuity speculation 253
65 Remarks on the observations 255
IV Dynamics and statistics 257
66 Goals 257
67 Definitions of variables and distribution functions 258
68 BBGKY hierarchy equations 259
69 Fluid limit 262
70 Evolution of the integral of ξ 264
71 Particle conservation equations 266
72 Relative peculiar velocity dispersion 272
73 Similarity solution 275
74 Cosmic energy equation 278
75 Cosmic virial theorem 280
76 Joint distribution in position and velocity 284
77 Behavior of the halo around a cluster of galaxies 291
78 Superclusters 299
79 Problems and prospects 301
V Relativistic theory of the behavior of irregularities in an expanding world model 304
80 Role of the relativistic theory 304
81 Time-orthogonal coordinates 306
82 The field equations for hαβ 310
83 Gravitational waves 312
84 Newtonian approximation 313
85 Linear perturbation equations for the matter 317
86 Behavior of density perturbations at wavelength » ct 319
87 Spherical model 324
88 Evolution of acoustic waves 330
89 Nonlinear acoustic waves 333
90 Incompressible flow 341
91 Behavior of collisionless particles 345
92 Linear dissipation of adiabatic perturbations 352
93 Residual fluctuations in the microwave background 363
94 Isothermal perturbations 373
VI Scenarios 379
95 Nature of the universe at high redshift 379
96 Nature of protogalaxies and protoclusters 384
Appendix 395
97 Models and notation 395
List of abbreviations 401
References 402
Index 417
