We perform a detailed study of dark matter production via freeze-in under the assumption that some fluid dominates the early Universe before depositing its energy to the plasma causing entropy injection. As a dark matter candidate we consider a fermionic singlet that is produced through its interactions with a scalar particle in the thermal plasma. The fluid alters the expansion rate of the Universe, as well as the scaling of the temperature, which significantly affects the evolution of both the number density and the mean momentum of the dark matter particle. We identify and discuss in detail the effects of the evolution of these quantities by considering several examples representing dark matter production at different stages of expansion and entropy injection. We find that, since the dark matter density is reduced when the entropy injection to the plasma continues after freeze-in, in order to reproduce its observational value an enhanced rate of dark matter production is required relative to standard cosmology. Furthermore, the impact of the assumed non-standard cosmological history on the dark matter mean momentum can result in either a relaxed or a tightened bound on the dark matter mass from large structure formation data.
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