# Density distribution of the cosmological matter field

## TL;DR

This paper provides a highly accurate, comprehensive analysis of the matter density PDF in the universe using extensive N-body simulations, revealing its simple shape and dependence on cosmological parameters.

## Contribution

It introduces a double-exponential approximation for the matter density PDF that outperforms previous models and combines it with the spherical infall model for precise, wide-range predictions.

## Key findings

- The PDF declines as a power-law with density, P~rho^(-2).
- The double-exponential approximation fits simulation data with few percent errors.
- The PDF depends on redshift and cosmological density parameter Omega_m.

## Abstract

The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering, massive production of mock galaxy catalogs, and testing predictions of cosmological models. Here we make a comprehensive analysis of the dark matter PDF using a suite of 7000 N-body simulations that covers a wide range of numerical and cosmological parameters. We find that the PDF has a simple shape: it declines with density as a power-law P~rho**(-2), which is exponentially suppressed on both small and large densities. The proposed double-exponential approximation provides an accurate fit to all our N-body results for small filtering scales R< 5Mpc/h with rms density fluctuations sigma>1. In combination with the spherical infall model that works well for small fluctuations sigma<1, the PDF is now approximated with just few percent errors over the range of twelve orders of magnitude -- a remarkable example of precision cosmology. We find that at 5-10% level the PDF explicitly depends on redshift (at fixed sigma) and on cosmological density parameter Omega_m. We test different existing analytical approximations and find that the often used log-normal approximation is always 3-5 times less accurate than either the double-exponential approximation or the spherical infall model.