Thick self-gravitating plane-symmetric domain walls

Abstract

We investigate a self-gravitating thick domain wall for a $λΦ^4$ 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 $ε$. For $ε\ll 1$, we find a domain wall solution by expanding the equations of motion around the flat spacetime kink. For ``large'' $ε$, we show analytically and numerically that only the de Sitter solution exists, and that there is a phase transition at some $ε_{\rm max}$ 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.