The position-dependent matter density probability distribution function

TL;DR

This paper introduces the position-dependent matter density PDF as a new cosmological observable, demonstrating its dependence on local density variations and providing a model validated by simulations.

Contribution

It proposes the position-dependent PDF as a novel, simpler-to-model cosmological probe and develops a linear response model validated through simulations.

Findings

The position-dependent PDF effectively captures local density variations.

The linear response model accurately predicts simulation results.

Separate universe simulations provide a lower variance estimate of the response.

Abstract

We introduce the position-dependent probability distribution function (PDF) of the smoothed matter field as a cosmological observable. In comparison to the PDF itself, the spatial variation of the position-dependent PDF is simpler to model and has distinct dependence on cosmological parameters. We demonstrate that the position-dependent PDF is characterized by variations in the local mean density, and we compute the linear response of the PDF to the local density using separate universe N-body simulations. The linear response of the PDF to the local density field can be thought of as the linear bias of regions of the matter field selected based on density. We provide a model for the linear response, which accurately predicts our simulation measurements. We also validate our results and test the separate universe consistency relation for the local PDF using global universe simulations. We find excellent agreement between the two, and we demonstrate that the separate universe method gives a lower variance determination of the linear response.