The central region of a void: an analytical solution

TL;DR

This paper derives an exact analytical equation for the central density of cosmic voids, revealing that their emptiness is overestimated in simulations and that dark energy influences their underdensity.

Contribution

It provides a new analytical solution for void central regions, clarifies the impact of initial perturbations and dark energy, and suggests improvements for N-body simulation models.

Findings

Void central density depends solely on initial perturbation amplitude.

Most voids should have a central underdensity greater than -73%.

Dark energy reduces the underdensity of voids.

Abstract

We offer an exact analytical equation for the void central region. We show that the central density is solely determined by the amplitude of the initial perturbation. Our results suggest that N-body simulations somewhat overestimate the emptiness of voids: the majority of them should have the central underdensity $\delta_c > -73\%$, and there should be almost no voids with $\delta_c < -88\%$. The central region of a void is a part of an open Friedmann's 'universe', and its evolution differs drastically from the Universe evolution: there is a long stage when the curvature term dominates, which prevents the formation of galaxy clusters and massive galaxies inside voids. The density profile in the void center should be very flat. We discuss some void models obtained by N-body simulations and offer some ways to improve them. We also show that the dark energy makes the voids less underdense.