  Light sterile neutrinos might mix with the active ones and be copiously
produced in the early Universe. In the present paper, a detailed multi-flavor
analysis of sterile neutrino production is performed. Making some justified
approximations allows us to consider not only neutrino interactions with the
primeval medium and neutrino coherence breaking effects, but also oscillation
effects arising from the presence of three light (mostly-active) neutrino
states mixed with two heavier (mostly-sterile) states. First, we emphasize the
underlying physics via an analytical description of sterile neutrino abundances
that is valid for cases with small mixing between active and sterile neutrinos.
Then, we study in detail the phenomenology of (3+2) sterile neutrino models in
light of short-baseline oscillation data, including the LSND and MiniBooNE
results. Finally, by using the information provided by this analysis, we obtain
the expected sterile neutrino cosmological abundances and then contrast them
with the most recent available data from Cosmic Microwave Background and Large
Scale Structure observations. We conclude that (3+2) models are significantly
more disfavored by the internal inconsistencies between sterile neutrino
interpretations of appearance and disappearance short-baseline data themselves,
rather than by the used cosmological data.
