Dark matter relic density in Gauss-Bonnet braneworld cosmology

The relic density of symmetric and asymmetric dark matter in a Gauss-Bonnet (GB) modified Randall-Sundrum (RS) type II braneworld cosmology is investigated. The existing study of symmetric dark matter in a GB braneworld (Okada and Okada, 2009) found that the expansion rate was reduced compared to that in standard General Relativity (GR), thereby delaying particle freeze-out and resulting in relic abundances which are suppressed by up to $\mathcal{O}(10^{-2})$. This is in direct contrast to the behaviour observed in RS braneworlds where the expansion rate is enhanced and the final relic abundance boosted. However, this finding that relic abundances are suppressed in a GB braneworld is based upon a highly contrived situation in which the GB era evolves directly into a standard GR era, rather than passing through a RS era as is the general situation. This collapse of the RS era requires equating the mass scale $m_{\alpha}$ of the GB modification and the mass scale $m_{\sigma}$ of the brane tension. However, if the GB contribution is to be considered as the lowest order correction from string theory to the RS action, we would expect $m_{\alpha} > m_{\sigma}$. We investigate the effect upon the relic abundance of choosing more realistic values for the ratio $\mathcal{R}_{m} \equiv m_{\alpha}/m_{\sigma}$ and find that the relic abundance can be either enhanced or suppressed by more than two orders of magnitude. However, suppression only occurs for a small range of parameter choices and, overwhelmingly, the predominant situation is that of enhancement as we recover the usual Randall-Sundrum type behaviour in the limit $\mathcal{R}_m \gg 1$. We use the latest observational bound $\Omega_{DM}h^2 = 0.1187 \pm 0.0017$ to constrain the various model parameters and briefly discuss the implications for direct/indirect dark matter detection experiments as well as dark matter particle models.