Gauss-Bonnet brane-world cosmology without $Z_{2}$-symmetry

TL;DR

This paper explores a brane-world cosmology with Gauss-Bonnet gravity on both sides of a non-symmetric brane, revealing modifications to the Friedmann equation and implications for early universe behavior and symmetry restoration.

Contribution

It introduces a model with asymmetric bulk spacetimes in Gauss-Bonnet gravity, analyzing how this affects junction conditions and cosmological evolution, especially the dominance of new terms.

Findings

New terms in Friedmann equation due to asymmetry.

Dominant terms behave like a cosmological constant at early times.

Asymmetry effects diminish at late times, restoring $Z_{2}$-symmetry.

Abstract

We consider a single 3-brane situated between two bulk spacetimes that posses the same cosmological constant, but whose metrics do not posses a $Z_{2}$-symmetry. On each side of the brane, the bulk is a solution to Gauss-Bonnet gravity. This asymmetry modifies junction conditions, and so new terms arise in the Friedmann equation. If these terms become dominant, these behave cosmological constant at early times for some case, and might remove the initial singularity for other case. However, we show that these new terms can not become dominant ones under usual conditions when our brane is outside an event horizon. We also show that any brane-world scenarios of this type revert to a $Z_{2}$-symmetric form at late times, and hence rule out certain proposed scenarios.