Evolution of thick domain walls in de Sitter universe

TL;DR

This paper investigates the evolution of thick domain walls in a de Sitter universe, revealing a critical thickness parameter that determines whether stationary solutions exist and analyzing the exponential growth of wall width beyond this threshold.

Contribution

It extends previous work by analyzing non-stationary domain wall evolution and identifying a critical thickness parameter affecting solution existence.

Findings

Stationary solutions exist for $\, ext{thickness} < H^{-1}/\sqrt{2}$.

No stationary solutions for $\, ext{thickness} \, ext{greater or equal to}$ $H^{-1}/\sqrt{2}$.

Wall width grows exponentially when thickness exceeds the critical value.

Abstract

We consider thick domain walls in a de Sitter universe following paper by Basu and Vilenkin. However, we are interested not only in stationary solutions found therein, but also investigate the general case of domain wall evolution with time. When the wall thickness parameter, $\delta_0$, is smaller than $H^{-1}/\sqrt{2}$, where $H$ is the Hubble parameter in de Sitter space-time, then the stationary solutions exist, and initial field configurations tend with time to the stationary ones. However, there are no stationary solutions for $\delta_0 \geq H^{-1}/\sqrt{2}$. We have calculated numerically the rate of the wall expansion in this case and have found that the width of the wall grows exponentially fast for $\delta_0 \gg H^{-1}$. An explanation for the critical value $\delta_{0c} = H^{-1}/\sqrt{2}$ is also proposed.