We assess the effects on big bang nucleosynthesis (BBN) of lepton number generation in the early universe resulting from the two-doublet four-neutrino mass-mixing scheme. It has been argued that this neutrino mass-mixing arrangement gives the most viable fit to the existing data. We study full $4\times 4$ mixing matrices and show how possible symmetries in these can affect the BBN ${}^4\mathrm{He}$ abundance yields. Though there is as yet no consensus on the reliability of BBN calculations with neutrino flavor mixing, we show that, in the case where the sign of the lepton number asymmetry is unpredictable, BBN considerations may pick out specific relationships between mixing angles. In particular, reconciling the observed light element abundances with a ${\overline{\nu }}_{\mu }\rightleftharpoons {\overline{\nu }}_e$ oscillation interpretation of LSND would allow unique new constraints on the neutrino mixing angles in this model.

• Received 6 August 1999

DOI:https://doi.org/10.1103/PhysRevD.62.093003