Inhomogeneous neutrino degeneracy and big bang nucleosynthesis - art. no. 083508

We examine big bang nucleosynthesis (BBN) in the case of inhomogeneous neut rino degeneracy, in the limit where the fluctuations are sufficiently small on large length scales that the present-day element abundances are homogen eous. We consider two representative cases: degeneracy of the electron neut rino alone and equal chemical potentials for all three neutrinos. We use a linear programming method to constrain an arbitrary distribution of the che mical potentials. For the current set of (highly restrictive) limits on the primordial element abundances, homogeneous neutrino degeneracy barely chan ges the allowed range of the baryon-to-photon ratio eta. Inhomogeneous dege neracy allows for little change in the lower bound on eta, but the upper bo und in this case can be as large as eta = 1.1 X 10(-8) (only v(e) degenerac y) or eta = 1.0 X 10(-9) (equal degeneracies for all three neutrinos). For the case of inhomogeneous neutrino degeneracy, we show that there is no BBN upper bound on the neutrino energy density, which is bounded in this case only by limits from structure formation and the cosmic microwave background .