Evolution of thick domain walls in inflationary and $p=w\rho$ universe

TL;DR

This paper investigates how thick domain walls evolve across different cosmological models, revealing that their growth or stabilization depends on a key time-dependent parameter related to the universe's expansion rate.

Contribution

It introduces a new analysis of domain wall evolution in various cosmological backgrounds, emphasizing the role of the parameter C(t) in determining their behavior.

Findings

For C(t)>2, the wall's thickness stabilizes at a microscopic scale.

For C(t)≤2, the wall expands and can become cosmologically large.

The evolution depends critically on the universe's equation of state and expansion rate.

Abstract

We study the evolution of thick domain walls in the different models of cosmological inflation, in the matter-dominated and radiation-dominated universe, or more generally in the universe with the equation of state $p=w\rho$. We have found that the domain wall evolution crucially depends on the time-dependent parameter $C(t)=1/(H(t)\delta_0)^2$, where $H(t)$ is the Hubble parameter and $\delta_0$ is the thickness of the wall in flat space-time. For $C(t)>2$ the physical thickness of the wall, $a(t)\delta(t)$, tends with time to $\delta_0$, which is microscopically small. Otherwise, when $C(t) \leq 2$, the wall steadily expands and can grow up to a cosmologically large size.