Simulating Rotating Newtonian Universes

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.