Brane cosmology with R_(4) term in the bulk

TL;DR

This paper investigates how adding a 4D Ricci scalar term to the 5D bulk action influences brane cosmology, leading to modified Einstein equations on the brane derived from bulk dynamics and junction conditions.

Contribution

It introduces a framework for deriving effective 4D Einstein equations in brane cosmology with an added intrinsic curvature term in the bulk action.

Findings

Modified energy-momentum tensor on the brane.

Consistent effective 4D Einstein equations derived.

Bulk geometry influences brane dynamics through junction conditions.

Abstract

We consider brane cosmology when the 4D Ricci scalar term is added to the 5D Einstein-Hilbert action and discuss the role that the addition of this term has on the brane-bulk system. The induced brane dynamics is shown to be the usual Einstein dynamics coupled to a modified energy-momentum tensor which is well defined once the 5D Einstein equations are solved in the bulk. The 5D Einstein equations valid everywhere in the bulk, but not in the brane, are projected on the brane. Then making use for the embedding of the brane in the bulk of the Israel junction conditions, modified by a source term coming from the addition of the intrinsic curvature scalar in the bulk action, it is possible to obtain the effective 4D Einstein equations on the brane consistent with the bulk geometry.