Evolution to a smooth universe in an ekpyrotic contracting phase with w > 1

TL;DR

This paper investigates the robustness of the ekpyrotic smoothing mechanism during a slow contraction phase with w > 1, demonstrating that it effectively homogenizes the universe even from highly inhomogeneous initial conditions.

Contribution

The study provides numerical evidence that the ekpyrotic phase can robustly smooth the universe starting from highly inhomogeneous and anisotropic states, confirming its effectiveness.

Findings

Regions become homogeneous and isotropic during the ekpyrotic phase

The ratio of smooth to non-smooth volume grows exponentially

Some regions retain anisotropic behavior with w=1

Abstract

A period of slow contraction with equation of state w > 1, known as an ekpyrotic phase, has been shown to flatten and smooth the universe if it begins the phase with small perturbations. In this paper, we explore how robust and powerful the ekpyrotic smoothing mechanism is by beginning with highly inhomogeneous and anisotropic initial conditions and numerically solving for the subsequent evolution of the universe. Our studies, based on a universe with gravity plus a scalar field with a negative exponential potential, show that some regions become homogeneous and isotropic while others exhibit inhomogeneous and anisotropic behavior in which the scalar field behaves like a fluid with w=1. We find that the ekpyrotic smoothing mechanism is robust in the sense that the ratio of the proper volume of the smooth to non-smooth region grows exponentially fast along time slices of constant mean curvature.