Generalized limits to the number of light particle degrees of freedom from big bang nucleosynthesis

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 Y_p = 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 N_ν based on the current best estimate of the primordial ⁴He abundance of Y_p = 0.238 is N_ν < 4.3 and varies from N_ν < 3.3 (at 95% C.L.) when Y_p = 0.225 to N_ν < 5.3 when Y_p = 0.250. If ⁷Li is depleted in these stars the upper limit to N_ν is relaxed. Taking (⁷Li/H)_p = 4.1 × 10⁻¹⁰, the limit varies from N_ν < 3.9 when Y_p = 0.225 to N_ν 6 when Y_p = 0.250. We also consider the consequences on the upper limit to N_ν if recent observations of deuterium in high-redshift quasar absorption-line systems are confirmed.