We point out that the baryon-number asymmetry in the Universe is erased by the sphaleron effect just below the electroweak phase transition irrespective of the primordial baryon- and lepton-number asymmetry, if there exists a Majorana-type interaction. The requirement to avoid this happening leads to the condition that $m_{\nu } \left(\mathrm{Majorana}\right)<\mathrm{}50\mathrm{}$ keV for all species of neutrions, regardless of whether or not neutrinos are stable.

• Received 14 May 1990

DOI:https://doi.org/10.1103/PhysRevD.42.1285