Matter power spectrum of light freeze-in dark matter: With or without self-interaction

We study the free-streaming effect in a light freeze-in dark matter model. Naturally in the dark sector one can find dark matter related coupling, and such coupling may induce dark matter self-scattering. In case that such scattering is subdominant, the dark matter partition function is not thermal but determined by the freeze-in process, yet its high momentum side is generally also Boltzmann suppressed. We show that the matter power spectrum is very similar to a warm dark matter one in shape. When matched to the current WDM bound, a 24 keV freeze-in dark matter is ruled out at 2 sigma confidence level. In case that the dark matter self-scattering is strong and decouples at a very late time, by a new numerical calculation we show that the early stage Brownian motion indeed protects the power spectrum against free-streaming suppression. However, such an effect cannot be characterized by a free-streaming length alone; we find that the self-scattering decoupling time is another necessary parameter. The currently interested dark matter self-interaction cross section similar to cm(2)/g is just marginal for such protection to be effective. (C) 2020 The Author. Published by Elsevier B.V.