Scalar-Tensor Gravity in Two 3-brane System

TL;DR

This paper derives the effective four-dimensional scalar-tensor gravity from a two 3-brane Randall-Sundrum model, showing how radion dynamics influence the gravitational theory and its convergence to Einstein gravity.

Contribution

It provides a detailed derivation of the low-energy effective action in the two-brane setup, revealing the dependence of the Brans-Dicke parameter on brane separation and radion fluctuations.

Findings

Effective action reduces to Brans-Dicke gravity with specific parameters.

Radion fluctuations affect the scalar-tensor nature of gravity.

Gravity on positive tension branes exhibits an attractor mechanism.

Abstract

We derive the low-energy effective action of four-dimensional gravity in the Randall-Sundrum scenario in which two 3-branes of opposite tension reside in a five-dimensional spacetime. The dimensional reduction with the Ansatz for the radion field by Charmousis et al., which solves five-dimensional linearized field equations, results in a class of scalar-tensor gravity theories. In the limit of vanishing radion fluctuations, the effective action reduces to the Brans-Dicke gravity in accord with the results of Garriga and Tanaka: Brans-Dicke gravity with the corresponding Brans-Dicke parameter $0< \omega < \infty$ (for positive tension brane) and $-3/2< \omega <0$ (for negative tension brane). In general the gravity induced a brane belongs to a class of scalar-tensor gravity with the Brans-Dicke parameter which is a function of the interval and the radion. In particular, gravity on a positive tension brane contains an attractor mechanism toward the Einstein gravity.