  We explore the implications of the existence of heavy neutral fermions (i.e.,
sterile neutrinos) for the thermal history of the early universe. In
particular, we consider sterile neutrinos with rest masses in the 100 MeV to
500 MeV range, with couplings to ordinary active neutrinos large enough to
guarantee thermal and chemical equilibrium at epochs in the early universe with
temperatures T > 1 GeV, but in a range to give decay lifetimes from seconds to
minutes. Such neutrinos would decouple early, with relic densities comparable
to those of photons, but decay out of equilibrium, with consequent prodigious
entropy generation prior to, or during, Big Bang Nucleosynthesis (BBN). Most of
the ranges of sterile neutrino rest mass and lifetime considered are at odds
with Cosmic Microwave Background (CMB) limits on the relativistic particle
contribution to energy density (e.g., as parameterized by N_eff). However, some
sterile neutrino parameters can lead to an acceptable N_eff. These parameter
ranges are accompanied by considerable dilution of the ordinary background
relic neutrinos, possibly an adverse effect on BBN, but sometimes fall in a
range which can explain measured neutrino masses in some particle physics
models. A robust signature of these sterile neutrinos would be a measured N_eff
not equal to 3 coupled with no cosmological signal for neutrino rest mass when
the detection thresholds for these probes are below laboratory-established
neutrino mass values, either as established by the atmospheric neutrino
oscillation scale or direct measurements with, e.g., KATRIN or neutrino-less
double beta decay experiments.
