Cosmological baryon and lepton number in the presence of electroweak fermion-number violation

In the presence of rapid fermion-number violation due to nonperturbative electroweak effects certain relations between the baryon number of the Universe and the lepton numbers of the Universe are predicted. In some cases the electron-neutrino asymmetry is exactly specified in terms of the baryon asymmetry. Without introducing new particles\char22{}beyond the usual quarks and leptons\char22{}it is necessary that the Universe possess a nonzero value of $B\ensuremath{-}L$ prior to the epoch of fermion-number violation if baryon and lepton asymmetries are to survive. Contrary to intuition, even though electroweak processes violate $B+L$, a nonzero value of $B+L$ persists after the epoch of rapid fermion-number violation. If the standard model is extended to include lepton-number violation, for example, through Majorana neutrino masses, then electroweak processes will reduce the baryon number to zero even in the presence of an initial $B\ensuremath{-}L$ unless $20{M}_{L}\ensuremath{\gtrsim}\sqrt{{T}_{B\ensuremath{-}L}{m}_{\mathrm{Pl}}}$ where ${M}_{L}$ sets the scale of lepton-number violation and ${T}_{B\ensuremath{-}L}$ is the temperature at which a $B\ensuremath{-}L$ asymmetry is produced. In some models this implies that neutrinos must be so light that they cannot contribute appreciably to the mass density of the Universe.