# Thick branes in higher-dimensional $f(R)$ gravity

## TL;DR

This paper investigates thick brane models in higher-dimensional $f(R)$ gravity, revealing conditions for regular solutions, their symmetry properties, and scalar field trapping, with both numerical and approximate analytical results.

## Contribution

It provides the first detailed analysis of thick branes in $f(R) o R^n$ gravity for $D
eq 4$, including existence conditions, symmetry properties, and scalar trapping.

## Key findings

- Regular vacuum solutions exist only for $1<n<D/2$.
- Solutions can be symmetric or nonsymmetric depending on boundary conditions.
- Scalar fields are trapped on the brane at any dimension.

## Abstract

We study the thick brane model within $f(R)\sim R^n$ modified gravity in $D$-dimensional spacetimes with $D\geq 6$. The system under consideration consists of two branes orthogonal to each other: the four-dimensional Lorentzian brane and $(D-5)$-dimensional Euclidean one. It is numerically shown that, for a given $D$, regular vacuum asymptotically anti-de Sitter solutions exist only in the range $1<n<D/2$. Depending on the values of $n$ and boundary conditions imposed on the Lorentzian brane, the solutions can pass or not pass through a fixed point located on the Lorentzian brane, and also be $Z_2$-symmetric or nonsymmetric. In the large-$D$ limit, we find approximate analytic solutions. It is also shown that a test scalar field is trapped on the Lorentzian brane at any $D$.