Lyman-$\alpha$ Forest Constraint on Dark Matter from Dark Sector Decay

By exploiting small-scale structure formation probed by Lyman-$\alpha$ forest observations, we study constraints on a model of dark matter from dark sector decay. We compute the phase space distribution of the dark matter and the linear matter power spectrum. We map the non-thermal dark matter distribution in this dark matter model to an approximate thermal warm dark matter distribution, and use this approximation to obtain a constraint from the Lyman-$\alpha$ forest observation. We combine the latest Lyman-$\alpha$ forest bounds with the constraint from the Big Bang Nucleosynthesis. As these two probes offer highly complementary constraints, we impose strong limits on sub-GeV dark matter. Consequently, masses lighter than $\sim 10^{-1}$ GeV are excluded, thereby significantly limiting the allowed parameter space. More broadly, our findings demonstrate the utility of small-scale structure observations in testing non-thermal dark matter paradigms, offering valuable insights for exploring a wider class of late-time decay models.