High-energy effective theory for matter on close Randall Sundrum branes

TL;DR

This paper develops an effective theory describing matter interactions on close Randall-Sundrum branes, capturing radion dynamics and gravitational effects, with implications for cosmology and Newtonian gravity.

Contribution

It provides a formal, all-orders derivative effective theory for brane matter-radion coupling in Randall-Sundrum models, including cosmological and perturbative analyses.

Findings

Effective radion-matter coupling expression derived.

The theory reproduces five-dimensional behavior in cosmological symmetry.

The Newtonian constant depends on brane separation and velocity.

Abstract

Extending the analysis of hep-th/0504128, we obtain a formal expression for the coupling between brane matter and the radion in a Randall-Sundrum braneworld. This effective theory is correct to all orders in derivatives of the radion in the limit of small brane separation, and, in particular, contains no higher than second derivatives. In the case of cosmological symmetry the theory can be obtained in closed form and reproduces the five-dimensional behaviour. Perturbations in the tensor and scalar sectors are then studied. When the branes are moving, the effective Newtonian constant on the brane is shown to depend both on the distance between the branes and on their velocity. In the small distance limit, we compute the exact dependence between the four-dimensional and the five-dimensional Newtonian constants.