Regge calculus models of closed lattice universes

TL;DR

This paper explores Regge calculus models of closed lattice universes with regular mass distributions, analyzing stability and perturbations to understand their evolution and stability conditions.

Contribution

It introduces a Regge calculus approach to model closed lattice universes with both uniform and perturbed mass distributions, highlighting stability criteria and evolution behavior.

Findings

Stable configurations require masses to be within specific spherical regions.

Perturbed universes show well-behaved evolution with increased expansion.

Dual Regge models are briefly discussed.

Abstract

This paper examines the behaviour of closed `lattice universes' wherein masses are distributed in a regular lattice on the Cauchy surfaces of closed vacuum universes. Such universes are approximated using a form of Regge calculus originally developed by Collins and Williams to model closed FLRW universes. We consider two types of lattice universes, one where all masses are identical to each other and another where one mass gets perturbed in magnitude. In the unperturbed universe, we consider the possible arrangements of the masses in the Regge Cauchy surfaces and demonstrate that the model will only be stable if each mass lies within some spherical region of convergence. We also briefly discuss the existence of Regge models that are dual to the ones we have considered. We then model a perturbed lattice universe and demonstrate that the model's evolution is well-behaved, with the expansion increasing in magnitude as the perturbation is increased.