We compute the big bang nucleosynthesis limit on the number of light neutrino degrees of freedom in a model-independent likelihood analysis based on the abundances of 4He and 7Li. We use the two-dimensional likelihood functions to simultaneously constrain the baryon-to-photon ratio and the number of light neutrinos for a range of 4He abundances Yp = 0.225-0.250, as well as a range in primordial 7Li abundances from (1.6 to 4.1) × 10-10. For (7Li/H)p = 1.6 × 10-10, as can be inferred from the 7Li data from Population II halo stars, the upper limit to Np based on the current best estimate of the primordial 4He abundance of Yp = 0.238 is Nν < 4.3 and varies from Nν < 3.3 (at 95% C.L.) when Yp = 0.225 to Nν < 5.3 when Yp = 0.250. If 7Li is depleted in these stars the upper limit to Nν is relaxed. Taking (7Li/H)p = 4.1 × 10-10, the limit varies from Nν < 3.9 when Yp = 0.225 to Nν ≲ 6 when Yp = 0.250. We also consider the consequences on the upper limit to Nν if recent observations of deuterium in high-redshift quasar absorption-line systems are confirmed.
Bibliographical noteFunding Information:
We note that this work was begun in collaboration with David Schramm.T his work was supportedi n part by DOE grant DE-FG02-94ER40823 at Minnesota.