# Precision Prediction for the Cosmological Density Distribution

## TL;DR

This paper develops an analytic model for the matter density distribution in the universe, focusing on skewness and using a GEV distribution to improve the lognormal approximation, achieving high accuracy across cosmological parameters.

## Contribution

It introduces a GEV-based model for the log density field that captures skewness and intrapixel correlations, enhancing the accuracy of cosmological matter distribution predictions.

## Key findings

- GEV distribution models the log density field with 1.7% accuracy
- Analytic fits for mean, variance, and skewness of the log density field
- Model applicable across various redshifts and smoothing scales

## Abstract

The distribution of matter in the universe is, to first order, lognormal. Improving this approximation requires characterization of the third moment (skewness) of the log density field. Thus, using Millennium Simulation phenomenology and building on previous work, we present analytic fits for the mean, variance, and skewness of the log density field $A$. We further show that a Generalized Extreme Value (GEV) distribution accurately models $A$; we submit that this GEV behavior is the result of strong intrapixel correlations, without which the smoothed distribution would tend (by the Central Limit Theorem) toward a Gaussian. Our GEV model yields cumulative distribution functions accurate to within 1.7 per cent for near-concordance cosmologies, over a range of redshifts and smoothing scales.