First investigation of void statistics in numerical relativity simulations

ABSTRACT We apply and extend standard tools for void statistics to cosmological simulations that solve Einstein’s equations with numerical relativity (NR). We obtain a simulated void catalogue without Newtonian approximations, using a new watershed void finder that operates on fluid-based NR simulations produced with the Einstein Toolkit. We compare and contrast measures of void size and void fraction, and compare radial stacked density profiles to empirically-derived Hamaus–Sutter–Wandelt (HSW) density profiles and profiles based on distance to void boundaries. We recover statistics roughly consistent with Newtonian N-body simulations where such a comparison is meaningful. We study the variation of dynamical spatial curvature and local expansion explicitly demonstrating the spatial fluctuations of these quantities in void regions. We find that voids in our simulations expand ∼10–30 per cent faster than the global average, and the spatial curvature density parameter in the centre of voids reaches ∼60–80 per cent.