Thick brane in Rastall gravity

TL;DR

This paper explores thick brane models within Rastall gravity, analyzing their stability and tensor perturbations across flat, de Sitter, and anti-de Sitter geometries, revealing conditions for localization and stability of tensor modes.

Contribution

It constructs and analyzes three types of maximally symmetric thick brane models in Rastall gravity, providing new insights into their stability and tensor mode localization.

Findings

Tensor modes are unstable or nonlocalizable in flat branes for nonzero Rastall parameter.

Only the ground tensor mode is localized in de Sitter branes.

Infinite bound tensor states exist in anti-de Sitter branes.

Abstract

In this work, thick branes in Rastall gravity are investigated. Three types of maximally symmetric thick brane models are constructed and the linear tensor perturbation is analyzed. In the flat brane model, the tensor modes of the perturbation are either unstable or nonlocalizable for a nonvanishing Rastall parameter. In the de Sitter brane model, only the ground state of the tensor mode is localized. In the anti-de Sitter brane model, the number of the bound tensor states is infinity. For both the de Sitter and anti-de Sitter brane models, the condition of stability for the Rastall parameter is obtained.