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Title:
Kurtosis and large-scale structure
Authors:
Catelan, Paolo; Moscardini, Lauro
Affiliation:
AA(SISSA, Trieste, Italy), AB(SISSA, Trieste, Italy)
Publication:
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 426, no. 1, p. 14-18 (ApJ Homepage)
Publication Date:
05/1994
Category:
Astrophysics
Origin:
STI
NASA/STI Keywords:
Astronomical Models, Cosmology, Density Distribution, Inflating, Kurtosis, Mass Distribution, Power Spectra, Skewness, Universe, Approximation, Differential Equations, Equations Of Motion, Fourier Transformation, Nonlinear Evolution Equations, Normal Density Functions, Statistical Analysis
DOI:
10.1086/174034
Bibliographic Code:
1994ApJ...426...14C

Abstract

We discuss the nonlinear growth of the excess kurtosis parameter of the smoothed density fluctuation field delta, S4 is defined as ((the mean value of (delta4)) - (3 x ((mean value of (delta2))2)))/((mean value of (delta2))3) in an Einstein-de Sitter universe. We assume Gaussian primordial density fluctuations with scale-free power spectrum P(k) varies as kn and analyze the dependence of S4 on primordial spectral index n, after smoothing with a Gaussian filter. As already known for the skewness ratio S3, the kurtosis parameter is a decreasing function of n, both in exact perturbative theory and in the Zel'dovich approximation. The parameter S4 provides a powerful statistic to test different cosmological scenarios.

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