A New Look At Neutrino Limits From Big Bang Nucleosynthesis

We take a fresh look at the limits on the number of neutrino flavors derived from big bang nucleosynthesis. In particular, recent measurements of the \he4 abundance enable one to estimate the primordial \he4 mass fraction at $Y_p = 0.232 \pm .003(stat) \pm .005(syst)$. For a baryon to photon ratio, $\eta$, consistent with the other light elements, this leads to a best fit for the number of neutrino flavors $N_\nu < 3$ (the precise number depends on $\eta$) indicating a very strong upper limit to $N_\nu$. Here, we derive new upper limits on $N_\nu$, paying special attention to the fact that the best estimate may lie in an unphysical region ($N_\nu < 3$ if all three neutrino flavors are light or massless; the lower bound to $N_\nu$ may even be as low as 2, if the small window for a $\nu_\tau$ mass is exploited.) Our resulting upper limits therefore depend on whether $N_\nu \ge 2$ or 3 is assumed. We also explore the sensitivity of our results to the adopted value of $\eta$ and the assumed systematic errors in $Y_p$.