Approximating Density Probability Distribution Functions Across Cosmologies

TL;DR

This paper develops a parameterized model for density probability distribution functions across different cosmologies using self-similar simulations, providing analytical fits and making the PDFs publicly available.

Contribution

It introduces a three-parameter model to accurately approximate density PDFs across various cosmologies, including LCDM, based on self-similar simulation data.

Findings

Density PDFs are well-described by two parameters in real space.

Adding a third parameter captures redshift-space and geometric mean PDFs.

The model enables approximation of PDFs for different cosmologies with analytical fits.

Abstract

Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: $n_s$, the spectral slope, and $\sigma_L$, the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, $s_L={\sqrt{\langle(dv^L_{\rm pec}/dr)^2\rangle}}/{H}$. We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.