Bulk scalar field in brane-worlds with induced gravity inspired by the ${\cal L}(R)$ term

TL;DR

This paper derives effective gravitational equations in a brane-world model with an ${ m extit{L}}(R)$ gravity term and a bulk scalar field, analyzing cosmological dynamics including Friedmann and acceleration equations.

Contribution

It introduces a novel framework combining ${ m extit{L}}(R)$ gravity and bulk scalar fields in brane-world scenarios, deriving key cosmological equations.

Findings

Friedmann equations are obtained for the ${ m R}^n$ gravity case.

Conditions for cosmic acceleration are derived.

The model extends previous brane-world theories with higher-order curvature terms.

Abstract

We obtain the effective field equations in a brane-world scenario within the framework of a DGP model where the action on the brane is an arbitrary function of the Ricci scalar, ${\cal L}(R)$, and the bulk action includes a scalar field in the matter Lagrangian. We obtain the Friedmann equations and acceleration conditions in the presence of the bulk scalar field for the $R^n$ term in four-dimensional gravity.