Thick self-gravitating plane-symmetric domain walls

TL;DR

This paper studies self-gravitating thick domain walls in a scalar field theory, revealing a phase transition between domain wall and de Sitter solutions depending on gravitational strength.

Contribution

It provides analytical and numerical analysis of solutions and identifies a phase transition related to the gravitational coupling parameter.

Findings

Existence of two solution types: domain walls and de Sitter spaces.

A critical gravitational strength psilon_{ m max}etermines the phase transition.

For small psilon,omain wall solutions are found; for large psilon,e Sitter solutions dominate.

Abstract

We investigate a self-gravitating thick domain wall for a $\lambda \Phi^4$ potential. The system of scalar and Einstein equations admits two types of non-trivial solutions: domain wall solutions and false vacuum-de Sitter solutions. The existence and stability of these solutions depends on the strength of the gravitational interaction of the scalar field, which is characterized by the number $\epsilon$. For $\epsilon \ll 1$, we find a domain wall solution by expanding the equations of motion around the flat spacetime kink. For ``large'' $\epsilon$, we show analytically and numerically that only the de Sitter solution exists, and that there is a phase transition at some $\epsilon_{\rm max}$ which separates the two kinds of solution. Finally, we comment on the existence of this phase transition and its relation to the topology of the domain wall spacetime.