Ultralocality and Slow Contraction

TL;DR

This paper investigates how slow contraction in the early universe leads to smoothing and flattening, revealing a two-stage process involving an ultralocal state followed by homogenization, using advanced numerical relativity simulations.

Contribution

It provides a detailed numerical analysis of the smoothing process in slow contraction, including non-perturbative initial conditions and the ultralocal to homogeneous transition.

Findings

Rapid convergence to an ultralocal, curved, and anisotropic state.

Subsequent decay to a homogeneous, flat, and isotropic spacetime.

Smoothing behavior is consistent whether entire spacetime or parts are considered.

Abstract

We study the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two independent spatial directions. Contrary to common descriptions of the early universe, we find that the geometry first rapidly converges to an inhomogeneous, spatially-curved and anisotropic ultralocal state in which all spatial gradient contributions to the equations of motion decrease as an exponential in time to negligible values. This is followed by a second stage in which the geometry converges to a homogeneous, spatially flat and isotropic spacetime. In particular, the decay appears to follow the same history whether the entire spacetime or only parts of it are smoothed by the end of slow contraction.