A de-Sitter thick domain wall solution by elliptic functions

TL;DR

This paper presents an exact analytical solution for a de-Sitter thick domain wall in five-dimensional Einstein gravity coupled with a scalar field, using elliptic functions to express the solution.

Contribution

It introduces a novel analytical solution involving elliptic functions for a de-Sitter thick domain wall with an axion-like scalar potential.

Findings

Solution expressed in terms of elliptic functions

Scalar potential is axion-like: V(phi)=a+b cos(phi)

Constants satisfy -3b<5a<3b

Abstract

We obtain and study an analytical solution of a de-Sitter thick domain wall in five-dimensional Einstein gravity interacting with a scalar field. The scalar field potential is axion-like, V(phi)=a+b cos(phi) with constants a,b satisfying -3b<5a<3b, and the solution is expressed in terms of elliptic functions.