Brane versus shell cosmologies in Einstein and Einstein-Gauss-Bonnet theories

TL;DR

This paper compares brane and shell cosmologies within Einstein and Einstein-Gauss-Bonnet theories, highlighting differences in early universe behavior and modifications to matching conditions due to higher-order curvature corrections.

Contribution

It introduces a shell cosmology model without Z2 symmetry and analyzes how Gauss-Bonnet corrections alter membrane matching conditions beyond Einstein's theory.

Findings

Shell model exhibits non-zero initial scale factor at big bang

Gauss-Bonnet corrections modify Israel matching conditions

Membrane physics may be absorbed into a renormalized Einstein constant

Abstract

We first illustrate on a simple example how, in existing brane cosmological models, the connection of a 'bulk' region to its mirror image creates matter on the 'brane'. Next, we present a cosmological model with no $Z_2$ symmetry which is a spherical symmetric 'shell' separating two metrically different 5-dimensional anti-de Sitter regions. We find that our model becomes Friedmannian at late times, like present brane models, but that its early time behaviour is very different: the scale factor grows from a non-zero value at the big bang singularity. We then show how the Israel matching conditions across the membrane (that is either a brane or a shell) have to be modified if more general equations than Einstein's, including a Gauss-Bonnet correction, hold in the bulk, as is likely to be the case in a low energy limit of string theory. We find that the membrane can then no longer be treated in the thin wall approximation. However its microphysics may, in some instances, be simply hidden in a renormalization of Einstein's constant, in which cases Einstein and Gauss-Bonnet membranes are identical.