Relic density and astrophysical signatures of MeV scale bound state dark matter

We study a strongly interacting complex scalar dark matter candidate, $χ$, interacting through an attractive potential mediated by a dark radiation $Φ$. Such interactions allow $χ$ to form bound states: SIMPonium. We systematically investigate the bound-state dynamics of this dark sector, including the formation and decay of SIMPonium and its impact on the thermal evolution of dark matter. We performed Monte Carlo simulations to compute the relic abundances of both free and bound state dark matter. We find that a successful freeze out of the dark sector requires a free dark matter yield of $Y_χ\sim 10^{-9}$ and SIMPonium yield of $Y_B \sim 10^{-13}$. The constraints from $ΔN_{\rm eff}$ reveal that only scalar mediated self interactions remain viable. For Higgs portal models, these constraints require the dark matter mass to satisfy $m_χ< 25~\mathrm{MeV}$. Within this mass range, indirect detection constraints imply that, for $g_χ> 10^{-2}$, the allowed range of the Higgs portal coupling is approximately $10^{-4} \lesssim λ\lesssim 10^{-2}$. For $g_χ< 10^{-2}$, the constraints are satisfied for a broader range, $10^{-4} \lesssim λ\lesssim 1$.