Freezing-in Cannibals with Low-reheating Temperature

The freeze-in mechanism provides a compelling framework for dark matter (DM) production, particularly suited to scenarios involving feeble interactions with the Standard Model (SM). In this work, we highlight a possible interplay of a non-instantaneous reheating phase and dark sector self-interactions, specifically $2 \to 3$ and $3 \to 2$ cannibalization processes. As an example we study the freeze-in production of a complex scalar DM candidate stabilized by a $\mathbb{Z}_3$ symmetry permitting cubic self-couplings, enabling number-changing interactions that drive internal thermalization and significantly modify the dark sector number density and temperature evolution. We numerically solve the coupled Boltzmann equations for the DM number density and temperature alongside the evolving SM bath, accurately capturing the dynamics of a prolonged reheating epoch. Our analysis reveals a rich and distinctive phenomenology arising from the interplay between the Universe's thermal history, Higgs portal mediated production, and cannibalistic self-interactions. Compared to scenarios with instantaneous reheating or negligible self-interactions, our framework opens new viable regions in parameter space, particularly for light DM, potentially within reach of future probes.