Thick Brane Worlds and Their Stability

TL;DR

This paper investigates three types of thick brane models in higher-dimensional gravity, analyzing their stability under scalar perturbations and finding that all are stable due to positive effective potentials.

Contribution

It introduces non-singular thick brane solutions with dilatons and potentials, and demonstrates their stability through scalar perturbation analysis.

Findings

All three brane types are stable under small scalar perturbations.

Effective potentials of the perturbation equations are positive definite.

The models are realized as solutions to Einstein equations with non-trivial dilatons.

Abstract

Three types of thick branes, i.e., Poincar\'{e}, de Sitter and Anti-de Sitter brane are considered. They are realized as the non-singular solutions of the Einstein equations with the non-trivial dilatons and the potentials. The scalar perturbations of these systems are also investigated. We find that the effective potentials of the master equations of the scalar perturbations are positive definite and consequently these systems are stable under the small perturbations.