The central region of a void: an analytical solution

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.