Thick domain wall universes

TL;DR

This paper classifies and analyzes thick gravitating domain wall solutions in various potentials, revealing two main solution types and their stability properties, with detailed numerical and analytical insights into their phase space and effects of cosmological constants.

Contribution

It provides a comprehensive classification of thick gravitating domain wall solutions and explores their stability and phase space using both analytical and numerical methods.

Findings

Two main solution categories: isolated domain walls with horizons and false vacuum de Sitter solutions.

False vacuum solutions are generally unstable but can form if scalar coupling to gravity is weak.

Numerical results agree well with analytical predictions across different models and cosmological constants.

Abstract

We investigate the spacetime of a thick gravitating domain wall for a general potential $V(\Phi)$. Using general analytical arguments we show that all nontrivial solutions fall into two categories: those interpretable as an isolated domain wall with a cosmological event horizon, and those which are pure false vacuum de Sitter solutions. Although this latter solution is always unstable to the field rolling coherently to its true vacuum, we show that there is an additional instability to wall formation if the scalar field does not couple too strongly to gravity. Using the $\lambda \Phi^4$ and sine-Gordon models as illustrative examples, we investigate the phase space of the gravitating domain wall in detail numerically, following the solutions from weak to strong gravity. We find excellent agreement with the analytic work. Then, we analyse the domain wall in the presence of a cosmological constant finding again the two kinds of solutions, wall and de Sitter, even in the presence of a negative cosmological constant.