High-Energy theory for close Randall Sundrum branes

TL;DR

This paper develops an effective high-energy theory for radion dynamics in the two-brane Randall Sundrum model, valid near brane collision, extending low-energy theories to include second-order velocity corrections.

Contribution

It introduces a recursive solution method for the bulk equations, resulting in a simple, high-energy effective theory that includes second derivatives and powers of first derivatives.

Findings

Effective radion theory valid at high energies and close brane separation.

Includes second derivatives and first derivative powers, simplifying solutions.

Extended theory with potential and brane detuning.

Abstract

We obtain an effective theory for the radion dynamics of the two-brane Randall Sundrum model, correct to all orders in brane velocity in the limit of close separation, which is of interest for studying brane collisions and early Universe cosmology. Obtained via a recursive solution of the Bulk equation of motions, the resulting theory represents a simple extension of the corresponding low-energy effective theory to the high energy regime. The four-dimensional low-energy theory is indeed not valid when corrections at second order in velocity are considered. This extension has the remarkable property of including only second derivatives and powers of first order derivatives. This important feature makes the theory particularly easy to solve. We then extend the theory by introducing a potential and detuning the branes.