Some thick brane solutions in $f(R)$-gravity

TL;DR

This paper explores thick brane solutions within $f(R) o R^n$ gravity, demonstrating the existence of regular asymptotically anti-de Sitter solutions and a fixed point that simplifies the model setup.

Contribution

It introduces a new class of thick brane solutions in $f(R)$ gravity with a fixed point feature that alleviates fine-tuning issues.

Findings

Existence of regular asymptotically anti-de Sitter solutions for certain $n$ values.

Identification of a fixed point in the phase space where solutions originate.

The fixed point enables placement of the brane without fine-tuning parameters.

Abstract

The thick brane model is considered in $f(R)\sim R^n$ gravity. It is shown that regular asymptotically anti-de Sitter solutions exist in some range of values of the parameter $n$. A peculiar feature of this model is the existence of a fixed point in the phase plane where all solutions start, and the brane can be placed at this point. The presence of the fixed point allows to avoid fine tuning of the model parameters to obtain thick brane solutions.