A hierarchy of voids: More ado about nothing

TL;DR

This paper refines the theoretical modeling of cosmic voids by incorporating a fully Eulerian framework and spatial correlations, significantly impacting predictions of void abundances in the universe.

Contribution

It introduces a new approach to modeling voids that accounts for correlations and uses an Eulerian perspective, improving the accuracy of void abundance predictions.

Findings

Void-in-cloud process impact varies with scale correlations.

Including correlations reduces predicted small void abundances.

Eulerian framework alters void evolution modeling.

Abstract

We extend earlier work on the problem of estimating the void-volume function -- the abundance and evolution of large voids which grow gravitationally in an expanding universe -- in two ways. The first removes an ambiguity about how the void-in-cloud process, which erases small voids, should be incorporated into the excursion set approach. The main technical change here is to think of voids within a fully Eulerian, rather than purely Lagrangian, framework. The second accounts for correlations between different spatial scales in the initial conditions. We provide numerical and analytical arguments showing how and why both changes modify the predicted abundances substantially. In particular, we show that the predicted importance of the void-in-cloud process depends strongly on whether or not one accounts for correlations between scales. With our new formulation, the void-in-cloud process dramatically reduces the predicted abundances of voids if such correlations are ignored, but only matters for the smallest voids in the more realistic case in which the spatial correlations are included.