Low energy effective gravitational equations on a Gauss-Bonnet brane

TL;DR

This paper derives simplified low-energy gravitational equations for a Gauss-Bonnet braneworld, revealing Einstein-like equations with correction terms, and applies them to cosmology, also discussing holographic implications.

Contribution

It provides a clear derivation of effective gravitational equations on a Gauss-Bonnet brane using a geometrical projection and gradient expansion, including cosmological applications.

Findings

Effective equations resemble Einstein equations with correction terms

Application to homogeneous and isotropic cosmology

Discussion of holographic interpretation

Abstract

We present effective gravitational equations at low energies in a $Z_2$-symmetric braneworld with the Gauss-Bonnet term. Our derivation is based on the geometrical projection approach, and we solve iteratively the bulk geometry using the gradient expansion scheme. Although the original field equations are quite complicated due to the presence of the Gauss-Bonnet term, our final result clearly has the form of the Einstein equations plus correction terms, which is simple enough to handle. As an application, we consider homogeneous and isotropic cosmology on the brane. We also comment on the holographic interpretation of bulk gravity in the Gauss-Bonnet braneworld.