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—beyond the usual quarks and leptons—it is necessary that the Universe possess a nonzero value of $B-L$ 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 $B-L$ unless $20M_L\gtrsim \sqrt{T_{B-L}{m}_{\mathrm{Pl}}}$ where $M_L$ sets the scale of lepton-number violation and $T_{B-L}$ is the temperature at which a $B-L$ 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.

• Received 25 May 1990

DOI:https://doi.org/10.1103/PhysRevD.42.3344