Codimension-1 thick brane solutions in higher-dimensional $R^n$ gravity

TL;DR

This paper derives vacuum solutions in higher-dimensional $R^n$ gravity that describe thick branes with codimension 1, analyzing how these solutions depend on parameters and showing they are asymptotically anti-de Sitter.

Contribution

It provides new explicit solutions for thick branes in $R^n$ gravity and studies their parameter dependence numerically, extending previous brane models.

Findings

Solutions tend to saturation as $eta$ increases.

Spacetime is asymptotically anti-de Sitter in all cases.

Parameter $eta$ influences the brane thickness and geometry.

Abstract

Vacuum plane symmetric solutions within $\alpha R^n$ modified gravity are obtained. The solutions can be regarded as describing thick branes with codimension 1 in a higher-dimensional spacetime. The dependence of the solutions on the values of four free parameters of the system under consideration is studied numerically. It is shown that when the parameter $\alpha$ increases, the solutions tend to saturation. We also show that in all cases under consideration the spacetime is asymptotically anti-de Sitter one.