Conserved currents in $D$-dimensional gravity and brane cosmology

TL;DR

This paper constructs conserved currents and superpotentials in D-dimensional gravity on curved backgrounds, highlighting their dependence on second derivatives and independence from added divergences, with applications to brane cosmology.

Contribution

It introduces conserved currents and superpotentials that depend on second derivatives and are divergence-independent, tailored for perturbations in Gauss-Bonnet brane cosmology.

Findings

Superpotentials depend on second derivatives in the Lagrangian.

Superpotentials are unaffected by divergences added to the Lagrangian.

Application to perturbations in Gauss-Bonnet cosmological brane models.

Abstract

In $D$-dimentional gravity on arbitrary curved backgrounds using proven methods conserved currents, divergences of antisymmetrical tensor densities (superpotentials), are constructed. These superpotentials have two remarkable properties: they depend in an essential way on second derivatives in the Lagrangian and are independent on divergences added to it. The conserved currents are thus particulary well adapted to the case of perturbations in Gauss-Bonett cosmological brane theories.