Graviton localization and Newton's law for brane models with a non-minimally coupled bulk scalar field

TL;DR

This paper investigates how a non-minimally coupled bulk scalar field affects graviton localization and the recovery of Newton's law in brane world models, highlighting the dependence on scalar field profiles and model parameters.

Contribution

It analyzes metric fluctuations in brane models with non-minimal scalar coupling and derives conditions for gravity localization and Newtonian behavior.

Findings

Localized zero mode depends on scalar field profile

General relativity is recovered under specific parameter restrictions

Solutions with RS warp factor are explicitly solved for point sources

Abstract

Brane world models with a non-minimally coupled bulk scalar field have been studied recently. In this paper we consider metric fluctuations around an arbitrary gravity-scalar background solution, and we show that the corresponding spectrum includes a localized zero mode which strongly depends on the profile of the background scalar field. For a special class of solutions, with a warp factor of the RS form, we solve the linearized Einstein equations, for a point-like mass source on the brane, by using the brane bending formalism. We see that general relativity on the brane is recovered only if we impose restrictions on the parameter space of the models under consideration.