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 ⁴He abundance enable one to estimate the primordial ⁴He mass fraction atY_p = 0.232 +/- 0.003 (stat) +/- 0.005 (syst). For a baryon to photon ratio, η, consistent with the other light elements, this leads to a best fit for the number of neutrino flavors N_v < 3 (the precise number depends on η) indicating a very strong upper limit toN_v . Here, we derive new upper limits on N_v, paying special attention to the fact that the best estimate may lie in an unphysical region (N_v < 3 if all three neutrino flavors are light or massless; the lower bound to N_v may even be as low as 2, if the small window for a v_τ mass is exploited). Our resulting upper limits therefore depend on whetherN_v >= 2 or 3 is assumed. We also explore the sensitivity of our results to the adopted value of η and the assumed systematic errors in Y_p.