Nucleosynthesis confronts an unstable, inert 17-keV state

We study the cosmological consequences of an inert 17-keV state mixing with the electron neutrino. We find that the nucleosynthesis upper bound on the primordial helium abundance prohibits the existence of such a state, unless its lifetime falls into the range 6×${10}^{\mathrm{-}4}$≲${\mathrm{\tau }}_{\mathrm{vac}}$≲2×${10}^{\mathrm{-}2}$ s. In this range the decay occurs after the chemical decoupling of the electron neutrinos and before the beginning of the nucleosynthesis, with the result that the predicted helium abundance can be lower than what it would be in the standard scenario.