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

May 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994aas...184.6206f&link_type=abstract

American Astronomical Society, 184th AAS Meeting, #62.06; Bulletin of the American Astronomical Society, Vol. 26, p.963

Mathematics

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Scientific paper

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 cannot be a good test of whether the density field is Gaussian.

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