Statistics of Primordial Density Perturbations from Discrete Seed Masses
Abstract
The statistics of density perturbations for general distributions of seed masses with arbitrary matter accretion is examined. Formal expressions for the power spectrum, the Npoint correlation functions, and the density distribution function are derived. These results are applied to the case of uncorrelated seed masses, and power spectra are derived for accretion of both hot and cold dark matter plus baryons. The reduced moments (cumulants) of the density distribution are computed and used to obtain a series expansion for the density distribution function. Analytic results are obtained for the density distribution function in the case of a distribution of seed masses with a spherical tophat accretion pattern. More generally, the formalism makes it possible to give a complete characterization of the statistical properties of any random field generated from a discrete linear superposition of kernels. In particular, the results can be applied to density fields derived by smoothing a discrete set of points with a window function.
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1991
 DOI:
 10.1086/170658
 Bibcode:
 1991ApJ...381..349S
 Keywords:

 Cosmology;
 Dark Matter;
 Space Density;
 Baryons;
 Density Wave Model;
 Mass;
 Perturbation Theory;
 Statistical Distributions;
 Astrophysics;
 COSMOLOGY;
 GALAXIES: CLUSTERING