Induced gravity with a non-minimally coupled scalar field on the brane

TL;DR

This paper derives four-dimensional cosmological equations for a brane-world with a non-minimally coupled scalar field, exploring solutions including de Sitter and conformally coupled cases, extending scalar-tensor gravity to higher dimensions.

Contribution

It introduces a brane-world model with a non-minimally coupled scalar field, analyzing its cosmological evolution and special solutions, extending scalar-tensor theories to five-dimensional brane scenarios.

Findings

Recovered four-dimensional evolution in low-energy and strong-coupling limits

Found de Sitter brane solutions with constant and evolving scalar fields

Identified conditions for a conventional Friedmann equation with conformal coupling

Abstract

We present the four-dimensional equations on a brane with a scalar field non-minimally coupled to the induced Ricci curvature, embedded in a five-dimensional bulk with a cosmological constant. This is a natural extension to a brane-world context of scalar-tensor (Brans-Dicke) gravity. In particular we consider the cosmological evolution of a homogeneous and isotropic (FRW) brane. We identify low-energy and strong-coupling limits in which we recover effectively four-dimensional evolution. We find de Sitter brane solutions with both constant and evolving scalar field. We also consider the special case of a conformally coupled scalar field for which it is possible (when the conformal energy density exactly cancels the effect of the bulk black hole) to recover a conventional four-dimensional Friedmann equation for all energy densities.