How empty are the voids?

TL;DR

This paper provides an analytical solution for the central matter density of cosmic voids, revealing that most voids are not as empty as previously thought, with their underdensity typically around 50%.

Contribution

It introduces an analytical model for the minimal matter density in voids, showing the relationship between void size and central underdensity, and clarifying the distribution of void emptiness.

Findings

Most voids have central underdensity around 50%.

Large voids always have less than 50% underdensity.

Void emptiness decreases with increasing size.

Abstract

We find an analytical solution for the minimal matter density of a void, its central density. It turns out that the voids are not so empty: most of the voids have the central underdensity $\Delta_c \sim -50\%$ (which means that the matter density in their centers is only two times lower than in the Universe on average). For small voids (of radius $R_0\simeq 5-10$~{Mpc}), the underdensity can be significantly greater, but the number of voids decreases rapidly with increasing of $|\Delta_c|$ over $50\%$, and voids with $\Delta_c < -80\%$ are practically absent. The large voids ($R_0\ge 40$~{Mpc}) always have $|\Delta_c| < 50\%$.