Evolution of a family of expanding cubic black-hole lattices in numerical relativity

TL;DR

This paper numerically evolves a family of expanding cubic black-hole lattices, demonstrating their cosmological scaling behavior and deviations from standard FLRW models through detailed simulations.

Contribution

It introduces a new numerical approach for evolving black-hole lattices and analyzes their cosmological properties over time.

Findings

Length scaling remains close to FLRW solutions during evolution.

Identifies significant departures from FLRW behavior in the simulations.

Develops a new multigrid solver for initial data computation.

Abstract

We present the numerical evolution of a family of conformally-flat, infinite, expanding cubic black-hole lattices. We solve for the initial data using an initial-data prescription presented recently, along with a new multigrid solver developed for this purpose. We then apply the standard tools of numerical relativity to calculate the time development of this initial dataset and derive quantities of cosmological relevance, such as the scaling of proper lengths. Similarly to the case of S3 lattices, we find that the length scaling remains close to the analytical solution for Friedmann-Lemaitre-Robertson-Walker cosmologies throughout our simulations, which span a window of about one order of magnitude in the growth of the scale factor. We highlight, however, a number of important departures from the Friedmann-Lemaitre-Robertson-Walker class.