We analyze the influence of decaying sterile neutrinos with the masses in the
range 1-140 MeV on the primordial Helium-4 abundance, explicitly solving the
Boltzmann equations for all particle species, taking into account neutrino
flavour oscillations, and paying special attention to systematic uncertainties.
We show that the Helium abundance depends only on the sterile neutrino lifetime
and not on the way the active-sterile mixing is distributed between flavours,
and derive an upper bound on the lifetime. We also demonstrate that the recent
results of Izotov & Thuan [arXiv:1001.4440], who find 2sigma higher than
predicted by the standard primordial nucleosynthesis value of Helium-4
abundance, are consistent with the presence in the plasma of sterile neutrinos
with the lifetime 0.01-2 seconds. The decay of these particles perturbs the
spectra of (decoupled) neutrinos and heats photons, changing the ratio of
neutrino to photon energy density, that can be interpreted as extra neutrino
species at the recombination epoch.Comment: 17 pp. + Appendices. Analysis of deuterium bounds and more accurate
account of CMB bounds on Helium-4 is added. Final version to appear in JCA
