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In many models of dark matter (DM), several production mechanisms contributeto its final abundance, often leading to a non-thermal momentum distribution.This makes it more difficult to assess whether such a model is consistent withstructure formation observations. We simulate the matter power spectrum for DMscenarios characterized by at least two temperatures and derive the suppressionof structures at small scales and the expected number of Milky Way dwarfgalaxies from it. This, together with the known bound on the number ofrelativistic particle species, $N_\mathrm{eff}$, allows us to obtainconstraints on the parameter space of non-thermally produced DM. We propose asimple parametrization for non-thermal DM distributions and present a fittingprocedure that can be used to adapt our results to other models.

Probing non-thermal light DM with structure formation and $N_\mathrm{eff}$