# New fitting formula for cosmic non-linear density distribution

## TL;DR

This paper introduces a new fitting formula, Nv2, for the cosmic matter density PDF, which outperforms the traditional log-normal model, especially in underdense regions, and captures non-Gaussian features across different scales and redshifts.

## Contribution

The paper proposes the Nv2 distribution as a superior fit for cosmic density PDFs, with detailed analysis of its parameters' evolution across scales and cosmologies.

## Key findings

- Nv2 fits cosmic density PDFs better than log-normal.
- Significant improvement in underdense regions.
- Parameters evolve with redshift and cosmology.

## Abstract

We have measured the probability distribution function (PDF) of cosmic matter density field from a suite of N-body simulations. We propose the generalized normal distribution of version 2 (Nv2) as an alternative fitting formula to the well-known log-normal distribution. We find that Nv2 provides significantly better fit than the log-normal distribution for all smoothing radii (2, 5, 10, 25 [Mpc/h]) that we studied. The improvement is substantial in the underdense regions. The development of non- Gaissianities in the cosmic matter density field is captured by continuous evolution of the skewness and shifts parameters of the Nv2 distribution. We present the redshift evolution of these parameters for aforementioned smoothing radii and various background cosmology models. All the PDFs measured from large and high-resolution N-body simulations that we use in this study can be obtained from a Web site at https://astro.kias.re.kr/jhshin.