f(R)-Brane

TL;DR

This paper explores brane solutions within modified f(R) gravity frameworks involving a scalar field and a single extra dimension, deriving first-order equations for constant curvature cases to facilitate analytical solutions.

Contribution

It introduces a method to find explicit brane solutions in f(R) gravity with scalar fields, simplifying the equations through first-order differential equations in constant curvature scenarios.

Findings

Derived first-order equations for constant curvature branes

Obtained explicit analytical solutions for specific f(R) models

Demonstrated the applicability of the method to current models

Abstract

We investigate the existence of brane solutions in braneworld scenarios described by real scalar field in the presence of modified $f(R)$ gravity with a single extra dimension. In the case of constant curvature, we obtain first-order differential equations which solve the equations of motion and ease the search for explicit analytical solutions. Several examples of current interest are investigated to illustrate the results of the present work.