Israel conditions for the Gauss-Bonnet theory and the Friedmann equation on the brane universe

TL;DR

This paper derives the Friedmann equation for a 3-brane universe within Einstein-Gauss-Bonnet gravity in higher dimensions, clarifying conflicting results in existing literature.

Contribution

It provides a consistent derivation of the Friedmann equation on a brane in Einstein-Gauss-Bonnet gravity, addressing previous contradictions.

Findings

Derived boundary conditions for Gauss-Bonnet gravity

Obtained Friedmann equation for 3-brane universe

Clarified conflicting results in literature

Abstract

Assuming an Einstein-Gauss-Bonnet theory of gravitation in a ($D \geq 5$)-dimensional spacetime with boundary, we consider the problem of the boundary dynamics given the matter Lagrangian on it. The resulting equation is applied in particular on the derivation of the Friedmann eq. of a 3-brane, understood as the non-orientable boundary of a 5d spacetime. We briefly discuss the contradictory conclusions of the literature.