We consider the effect of inhomogeneous neutrino degeneracy on big bang nucleosynthesis for the case where the distribution of neutrino chemical potentials is given by a Gaussian. The chemical potential fluctuations are taken to be isocurvature, so that only inhomogeneities in the electron chemical potential are relevant. Then the final element abundances are a function only of the baryon-photon ratio $\eta ,$ the effective number of additional neutrinos $\Delta N_{\nu },$ the mean electron neutrino degeneracy parameter $\overline{\xi },$ and the rms fluctuation of the degeneracy parameter, ${\sigma }_{\xi }.$ We find that for fixed $\eta ,$ $\Delta N_{\nu },$ and $\overline{\xi },$ the abundances of ${}^4\mathrm{He},$ D, and ${}^7\mathrm{Li}$ are, in general, increasing functions of ${\sigma }_{\xi }.$ Hence, the effect of adding a Gaussian distribution for the electron neutrino degeneracy parameter is to decrease the allowed range for $\eta .$ We show that this result can be generalized to a wide variety of distributions for $\xi .$

• Received 12 June 2002

DOI:https://doi.org/10.1103/PhysRevD.66.043531