Effective actions of a Gauss-Bonnet brane world with brane curvature terms

TL;DR

This paper analyzes a warped brane world with Gauss-Bonnet gravity and localized curvature, revealing how gravity behaves differently across energy regimes and highlighting limitations of the moduli approximation at low energy.

Contribution

It provides a detailed analysis of gravitational behavior in a Gauss-Bonnet brane world with localized curvature terms across various energy regimes, including the failure of the moduli approximation.

Findings

Gravity is four-dimensional at very high energy for positive tension brane.

Gravity appears five-dimensional at intermediate energy regimes.

At low energy, matter couples to gravity with a Brans-Dicke-like behavior.

Abstract

We consider a warped brane world scenario with two branes, Gauss-Bonnet gravity in the bulk, and brane localised curvature terms. When matter is present on both branes, we investigate the linear equations of motion and distinguish three regimes. At very high energy and for an observer on the positive tension brane, gravity is four dimensional and coupled to the brane bending mode in a Brans-Dicke fashion. The coupling to matter and brane bending on the negative tension brane is exponentially suppressed. In an intermediate regime, gravity appears to be five dimensional while the brane bending mode remains four dimensional. At low energy, matter on both branes couple to gravity for an observer on the positive tension brane, with a Brans-Dicke description similar to the 2--brane Randall-Sundrum setup. We also consider the zero mode truncation at low energy and show that the moduli approximation fails to reproduce the low energy action.