Dark matter relic density in scalar-tensor gravity revisited

We revisit the calculation of dark matter relic abundances in scalar-tensor gravity using a generic form $A({\phi }_{\ast })=e^{\beta {\phi }_{\ast }^2\mathrm{/}2}$ for the coupling between the scalar field ${\phi }_{\ast }$ and the metric, for which detailed Big Bang Nucleosynthesis constraints are available. We find that BBN constraints restrict the modified expansion rate in these models to be almost degenerate with the standard expansion history at the time of dark matter decoupling. In this case the maximum level of enhancement of the dark matter relic density was found to be a factor of $\sim 3$, several orders of magnitude below that found in previous investigations.