  Sterile neutrinos with mass ~1 eV and order 10% mixing with active neutrinos
have been proposed as a solution to anomalies in neutrino oscillation data, but
are tightly constrained by cosmological limits. It was recently shown that
these constraints are avoided if sterile neutrinos couple to a new MeV-scale
gauge boson A'. However, even this scenario is restricted by structure
formation constraints when A'-mediated collisional processes lead to efficient
active-to-sterile neutrino conversion after neutrinos have decoupled. In view
of this, we reevaluate in this paper the viability of sterile neutrinos with
such "secret" interactions. We carefully dissect their evolution in the early
Universe, including the various production channels and the expected
modifications to large scale structure formation. We argue that there are two
regions in parameter space - one at very small A' coupling, one at relatively
large A' coupling - where all constraints from big bang nucleosynthesis (BBN),
cosmic microwave background (CMB), and large scale structure (LSS) data are
satisfied. Interestingly, the large A' coupling region is precisely the region
that was previously shown to have potentially important consequences for the
small scale structure of dark matter halos if the A' boson couples also to the
dark matter in the Universe.
