Gravity in the Einstein-Gauss-Bonnet Theory with the Randall-Sundrum Background

TL;DR

This paper derives the 5D graviton propagator in the Randall-Sundrum model with Gauss-Bonnet interaction, showing how gravity localizes on the brane and analyzing conditions for ghost-free, Newtonian gravity.

Contribution

It provides the full graviton propagator in the RS model with Gauss-Bonnet term and explores the implications for gravity localization and ghost-free conditions.

Findings

Gravity localizes on the brane with Gauss-Bonnet term

Negative Gauss-Bonnet coefficient ensures ghost-free, Newtonian gravity

Reproduction of 4D Einstein gravity with brane bending for zero Gauss-Bonnet coefficient

Abstract

We obtain the full 5D graviton propagator in the Randall-Sundrum model with the Gauss-Bonnet interaction. From the decomposition of the graviton propagator on the brane, we show that localization of gravity arises in the presence of the Gauss-Bonnet term. We also obtain the metric perturbation for observers on the brane with considering the brane bending and compute the amplitude of one massless graviton exchange. For the positive definite amplitude or no ghost states, the sign of the Gauss-Bonnet coefficient should be negative in our convention, which is compatible with string amplitude computations. In that case, the ghost-free condition is sufficient for obtaining the Newtonian gravity. For a vanishing Gauss-Bonnet coefficient, the brane bending allows us to reproduce the correct graviton polarizations for the effective 4D Einstein gravity.