# The Void Size Function in Dynamical Dark Energy Cosmologies

## TL;DR

This paper validates a theoretical model of the void size distribution against large cosmological simulations with various dark energy equations of state, showing it can reliably constrain dark energy properties from observational data.

## Contribution

It demonstrates that the Sheth & van de Weygaert formalism accurately predicts void sizes across different dark energy models, supporting its use in observational constraints.

## Key findings

- The model matches simulation data within statistical errors for all tested dark energy models.
- The void size function remains accurate regardless of the void formation threshold.
- The theoretical model is robust and applicable to real observational data for dark energy studies.

## Abstract

We test a theoretical description of the void size distribution function against direct estimates from halo catalogues of the DEMNUni suite of large cosmological simulations. Besides standard $\Lambda$CDM, we consider deviations of the dark energy equation of state from $w=-1$, corresponding to four combinations in the popular Chevallier-Polarski-Linder parametrisation: $w_0=-0.9;-1.1$, $w_a=-0.3;0.3$. The theoretical void size function model, relying on the Sheth & van de Weygaert double barrier excursion set formalism, provides an accurate description of the simulation measurements for the different dark energy models considered, within the statistical errors. The model remains accurate for any value of the threshold for void formation $\delta_\mathrm{v}$. Its robust consistency with simulations demonstrates that the theoretical void size function can be applied to real data as a sensitive tool to constrain dark energy.