Distributions of Fourier Modes of Cosmological Density Fields

Abstract

We discuss the probability distributions of Fourier modes of cosmological density fields using the central limit theorem as it applies to weighted integrals of random fields. It is shown that if the cosmological principle holds in a certain sense, i.e., the universe approaches homogeneity and isotropy sufficiently rapidly on very large scales, the one-point distribution of each Fourier mode of the density field is Gaussian whether or not the density field itself is Gaussian. Therefore, one-point distributions of the power spectrum obtained from observational data or from simulations are not a good test of whether the density field is Gaussian.

accepted for publication in The Physical Review D. 28 pages, no figures. Tex file using wbasict.tex macros (appended at beginning of the paper)

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• Power Spectrum Analysis of Three-Dimensional Redshift Surveys
• $\Pi$ in the Sky ? Microwave Anisotropies from Cosmic Defects
• The Fourier Space Statistics of Seedlike Cosmological Perturbations

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