Fate of domain walls in 5D gravitational theory with compact extra dimension

TL;DR

This study numerically investigates the evolution of domain walls in a 5D gravitational framework with a compact extra dimension, revealing conditions for expansion or collapse depending on initial parameters and potential minima.

Contribution

It introduces a topological winding to prevent decay into vacuum and demonstrates the absence of static solutions, analyzing late-time behaviors in a 5D gravitational setting.

Findings

Both 3D space and extra dimension expand if initial Hubble parameter is positive.

The wall width remains nearly constant during evolution.

In other cases, the extra dimension diverges and the 3D space collapses.

Abstract

We pursue the time evolution of the domain walls in 5D gravitational theory with a compact extra dimension by numerical calculation. In order to avoid a kink-antikink pair that decays into the vacuum, we introduce a topological winding in the field space. In contrast to the case of non-gravitational theories, there is no static domain-wall solution in the setup. In the case that the minimal value of the potential is non-negative, we find that both the 3D space and the extra dimension will expand at late times if the initial value of the Hubble parameter is chosen as positive. The wall width almost remains constant during the evolution. In other cases, the extra dimension diverges and the 3D space shrinks to zero at a finite time.