The Effects of Multiple Modes and Reduced Symmetry on the Rapidity and Robustness of Slow Contraction

TL;DR

This study shows that increasing the number of spatial modes and reducing symmetry in initial conditions enhances the speed and robustness of slow contraction in homogenizing the universe, especially due to shear effects.

Contribution

It demonstrates that allowing initial variations along multiple spatial directions and modes improves the effectiveness of slow contraction, revealing new dynamics involving shear effects.

Findings

Enhanced rapidity and robustness with multi-directional variations

Shear effects become significant with multi-dimensional initial conditions

More degrees of freedom drive spacetime towards stable cosmological fixed points

Abstract

We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single fourier mode along only a single spatial direction are in general enhanced if the initial variations are along two spatial directions, include multiple modes, and thereby have reduced symmetry. Particularly significant are shear effects that only become possible when variations are allowed along two or more spatial dimensions. Based on the numerical results, we conjecture that the counterintuitive enhancement occurs because more degrees of freedom are activated which drive spacetime away from an unstable Kasner fixed point and towards the stable Friedmann-Robertson-Walker fixed point.