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We explore the implications of the existence of heavy neutral fermions (i.e.,sterile neutrinos) for the thermal history of the early universe. Inparticular, we consider sterile neutrinos with rest masses in the 100 MeV to500 MeV range, with couplings to ordinary active neutrinos large enough toguarantee thermal and chemical equilibrium at epochs in the early universe withtemperatures T > 1 GeV, but in a range to give decay lifetimes from seconds tominutes. Such neutrinos would decouple early, with relic densities comparableto those of photons, but decay out of equilibrium, with consequent prodigiousentropy generation prior to, or during, Big Bang Nucleosynthesis (BBN). Most ofthe ranges of sterile neutrino rest mass and lifetime considered are at oddswith Cosmic Microwave Background (CMB) limits on the relativistic particlecontribution to energy density (e.g., as parameterized by N_eff). However, somesterile neutrino parameters can lead to an acceptable N_eff. These parameterranges are accompanied by considerable dilution of the ordinary backgroundrelic neutrinos, possibly an adverse effect on BBN, but sometimes fall in arange which can explain measured neutrino masses in some particle physicsmodels. A robust signature of these sterile neutrinos would be a measured N_effnot equal to 3 coupled with no cosmological signal for neutrino rest mass whenthe detection thresholds for these probes are below laboratory-establishedneutrino mass values, either as established by the atmospheric neutrinooscillation scale or direct measurements with, e.g., KATRIN or neutrino-lessdouble beta decay experiments.

Heavy sterile neutrinos, entropy and relativistic energy production, and the relic neutrino background