HOMOGENEITY AND CLUSTERING
3
Physical principles
11
How did galaxies and clusters of galaxies form?
18
Summary
35
NEWTONIAN APPROXIMATION
37
Particle dynamics in expanding coordinates
41
The peculiar acceleration
43
the Vlasov equation and the ideal fluid
45
Relation between t and w some examples
195
Inversion of the equation
200
Angular threepoint correlation function
203
Angular fourpoint correlation function
209
Correction for curvature and expansion
213
Summary of numerical results
221
Power spectrum of the extragalactic light
225
Moments of the number of neighbors
230
Linear perturbation approximation for 5
49
p A 0
56
models with A 0
59
The peculiar velocity field
63
Joining conditions for d and v
66
Critical Jeans length
68
Primeval magnetic field as a source for Spp
71
Second order perturbation theory for 5pp
74
Spherical model
77
Homogeneous ellipsoid model
86
Caustics and pancakes
95
Expansion vorticity and shear
103
Origin of the rotation of galaxies
107
Cosmic energy equation
110
Spherical accretion model
115
Hierarchical clustering model
120
Fourier transform of the equations of motion
124
Coupling of density fluctuations
128
DESCRIPTIVE STATISTICS
138
Fair sample hypothesis
142
Twopoint spatial correlation function tr
143
another definition
145
Poisson model
147
Threepoint correlation function
148
Fourpoint correlation function
150
Moments of counts of objects
152
Constraints on t and f
156
Probability generating function
158
Estimates of PN
160
Cluster model
163
Power spectrum
166
Power law model for the spectrum
169
Bispectrum
171
Cross correlation function
172
Angular twopoint correlation function
174
Angular power spectrum
175
Estimating w6
183
Statistical uncertainty in the estimate of w0
187
Relation between angular and spatial twopoint correlation functions
189
Small separation approximation and the scaling relation
191
Decoupling of magnitude and position
194
Relation between t and w some examples
195
Inversion of the equation
200
Angular threepoint correlation function
203
Angular fourpoint correlation function
209
Correction for curvature and expansion
213
Summary of numerical results
221
Power spectrum of the extragalactic light
225
Moments of the number of neighbors
230
Model for PN
233
Clustering models
236
Mandelbrots prescription
243
The mass correlation functions
249
continuity speculation
253
Remarks on the observations
255
DYNAMICS AND STATISTICS
257
Definitions of variables and distribution functions
258
BBGKY hierarchy equations
259
Fluid limit
262
Evolution of the integral of
264
Particle conservation equations
266
Relative peculiar velocity dispersion
272
Similarity solution
275
Cosmic energy equation
278
Cosmic virial theorem
280
Joint distribution in position and velocity
285
Behavior of the halo around a cluster of galaxies
291
Superclusters
299
Problems and prospects
301
RELATIVISTIC THEORY OF THE BEHAVIOR OF IRREGULARITIES IN AN EXPANDING WORLD MODEL
304
Timeorthogonal coordinates
306
The field equations for haf
310
Gravitational waves
312
Newtonian approximation
313
Linear perturbation equations for the matter
317
Behavior of density perturbations at wavelength ct
319
Spherical model
324
Evolution of acoustic waves
330
Nonlinear acoustic waves
333
Incompressible flow
341
Behavior of collisionless particles
345
Linear dissipation of adiabatic perturbations
352
Residual fluctuations in the microwave background
363
Isothermal perturbations
373
SCENARIOS
379
Nature of protogalaxies and protoclusters
384
APPENDIX
395
LIST OF ABBREVIATIONS
401
INDEX
417
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