Low-energy effective theory for a Randall-Sundrum scenario with a moving bulk brane

TL;DR

This paper develops a low-energy effective gravitational theory for a generalized Randall-Sundrum model with a moving brane, resulting in a Brans-Dicke type theory with two scalar fields that couple to matter.

Contribution

It derives the first-order effective field equations for a three-brane setup with a moving bulk brane, extending previous models to include brane motion and scalar fields.

Findings

Effective theory is a generalized Brans-Dicke model with two scalar fields.

The theory is conformally equivalent to Einstein gravity with scalar fields.

Derived junction conditions for the Weyl tensor and extrinsic curvature.

Abstract

We derive the low-energy effective theory of gravity for a generalized Randall-Sundrum scenario, allowing for a third self-gravitating brane to live in the 5D bulk spacetime. At zero order the 5D spacetime is composed of two slices of anti-de Sitter spacetime, each with a different curvature scale, and the 5D Weyl tensor vanishes. Two boundary branes are at the fixed points of the orbifold whereas the third brane is free to move in the bulk. At first order, the third brane breaks the otherwise continuous evolution of the projection of the Weyl tensor normal to the branes. We derive a junction condition for the projected Weyl tensor across the bulk brane, and combining this constraint with the junction condition for the extrinsic curvature tensor, allows us to derive the first-order field equations on the middle brane. The effective theory is a generalized Brans-Dicke theory with two scalar fields. This is conformally equivalent to Einstein gravity and two scalar fields, minimally coupled to the geometry, but nonminimally coupled to matter on the three branes.