  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.
