Ellipsoidal collapse and the redshift space probability distribution function of dark matter

TL;DR

This paper develops a model based on ellipsoidal collapse physics to predict the probability distribution function of dark matter density in real and redshift space, aligning well with simulation data.

Contribution

It introduces a simple approximation to the ellipsoidal collapse model that extends real-space PDF predictions to redshift space, improving understanding of dark matter clustering.

Findings

Model accurately predicts redshift space PDF in simulations

Extension of real-space PDF to redshift space

Method recovers initial Gaussian PDF under certain conditions

Abstract

We use the physics of ellipsoidal collapse to model the probability distribution function of the smoothed dark matter density field in real and redshift space. We provide a simple approximation to the exact collapse model which shows clearly how the evolution can be thought of as a modification of the spherical evolution model as well as of the Zeldovich Approximation. In essence, our model specifies how the initial smoothed overdensity and shear fields can be used to determine the shape and size of the region at later times. We use our parametrization to extend previous work on the real-space PDF so that it predicts the redshift space PDF as well. Our results are in good agreement with measurements of the PDF in simulations of clustering from Gaussian initial conditions down to scales on which the rms fluctuation is slightly greater than unity. We also show how the highly non-Gaussian non-linear redshifted density field in a numerical simulation can be transformed so that it provides an estimate of the shape of the initial real-space PDF. When applied to our simulations, our method recovers the initial Gaussian PDF, provided the variance in the nonlinear smoothed field is less than 4.