Dynamic Dilatonic Domain Walls

TL;DR

This paper explores the dynamics of domain walls coupled to bulk matter in higher-dimensional theories, revealing conditions for static solutions, analyzing singular bulk geometries, and deriving cosmological models with inflationary behavior.

Contribution

It introduces a method to find static solutions for domain walls coupled to dilaton fields, and applies it to generate cosmological models within Hořava-Witten theory.

Findings

Bulk solutions can be static or time-dependent with horizons.

Significant world volume inflation occurs under certain potential conditions.

The approach yields cosmological solutions in string-inspired models.

Abstract

Motivated by the ``universe as a brane'' idea, we investigate the motion of a $(D-2)$-brane (or domain wall) that couples to bulk matter. Usually one would expect the spacetime outside such a wall to be time dependent however we show that in certain cases it can be static, with consistency of the Israel equations yielding relationships between the bulk metric and matter that can be used as ans\"atze to solve the Einstein equations. As a concrete model we study a domain wall coupled to a bulk dilaton with Liouville potentials for the dilaton both in the bulk and on the wall. The bulk solutions we find are all singular but some have black hole or cosmological horizons, beyond which our solutions describe domain walls moving in time dependent bulks. A significant period of world volume inflation occurs if the potential on the wall is not too steep; in some cases the bulk also inflates (with the wall comoving) while in others the wall moves relative to a non-inflating bulk. We apply our method to obtain cosmological solutions of Ho\v{r}ava-Witten theory compactified on a Calabi-Yau space. tive to a non-inflating bulk. We apply our method to obtain cosmological solutions of Ho\v{r}ava-Witten theory compactified on a Calabi-Yau space.