Distributions of Fourier Modes of Cosmological Density Fields

Details Distributions of Fourier Modes of Cosmological Density Fields Distributions of Fourier Modes of Cosmological Density Fields

1995-05-04

arxiv.org/abs/astro-ph/9505017v1

Phys.Rev. D51 (1995) 6714-6721

Astronomy and Astrophysics

Astrophysics

accepted for publication in The Physical Review D. 28 pages, no figures. Tex file using wbasict.tex macros (appended at beginn

Scientific paper

10.1103/PhysRevD.51.6714

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.

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