Simulating Rotating Newtonian Universes

TL;DR

This paper introduces a novel numerical simulation method for rotating universes based on a G"{o}del-like metric, revealing anisotropic expansion effects in cosmological models.

Contribution

It develops a new simulation approach using StePS to model rotating universes in infinite space, overcoming previous topological limitations.

Findings

Detected over 1% anisotropy in expansion rates due to rotation

Simulated rotation effects in Einstein-de Sitter and DM cosmologies

Maximal rotation without closed timelike curves identified

Abstract

We present the results of a novel type of numerical simulation that realizes a rotating Universe with a shear-free, rigid body rotation inspired by a G\"{o}del-like metric. We run cosmological simulations of unperturbed glasses with various degrees of rotation in the Einstein-de Sitter and the $\Lambda$CDM cosmologies. To achieve this, we use the StePS N-body code capable of simulating the infinite Universe, overcoming the technical obstacles of classical toroidal (periodic) topologies that would otherwise prevent us from running such simulations. Results show a clear anisotropy between the polar and equatorial expansion rates with more than $1\%$ deviation from the isotropic case for maximal rotation without closed timeline curves within the horizon, $\omega_{0} \approx 10^{-3}$ Gyr$^{-1}$; a considerable effect in the era of precision cosmology.