  We study production of self-interacting dark matter (DM) during an early
matter-dominated phase. As a benchmark scenario, we consider a model where the
DM consists of singlet scalar particles coupled to the visible Standard Model
(SM) sector via the Higgs portal. We consider scenarios where the initial DM
abundance is set by either the usual thermal freeze-out or an alternative
freeze-in mechanism, where DM was never in thermal equilibrium with the SM
sector. For the first time, we take the effect of self-interactions within the
hidden sector into account in determining the DM abundance, reminiscent to the
Strongly Interacting Massive Particle (SIMP) scenario. In all cases, the number
density of DM may change considerably compared to the standard
radiation-dominated case, having important observational and experimental
ramifications.
