About One-point Statistics of the Ratio of Two Fourier-transformed Cosmic Fields and an Application

TL;DR

This paper investigates the one-point statistics of the ratio of two Fourier-transformed cosmic fields, demonstrating that Gaussian-based models accurately describe the growth of dark matter density fluctuations in Fourier space.

Contribution

It introduces the distribution function of the ratio of two complex Gaussian variables and applies statistical models to analyze Fourier mode growth in cosmic fields.

Findings

Gaussian approximation models are highly accurate for one-point statistics.

The distribution of the ratio of two complex Gaussian variables is characterized.

Insights into dark matter density fluctuation growth in Fourier space are revealed.

Abstract

The Fourier transformation is an effective and efficient operation of Gaussianization at the one-point level. Using a set of N-body simulation data, we verified that the one-point distribution functions of the dark matter momentum divergence and density fields closely follow complex Gaussian distributions. The one-point distribution function of the quotient of two complex Gaussian variables is introduced and studied. Statistical theories are then applied to model one-point statistics about the growth of individual Fourier mode of the dark matter density field, which can be obtained by the ratio of two Fourier transformed cosmic fields. Our simulation results proved that the models based on the Gaussian approximation are impressively accurate, and our analysis revealed many interesting aspects about the growth of dark matter's density fluctuation in Fourier space.