Generalized Limits to the Number of Light Particle Degrees of Freedom from Big Bang Nucleosynthesis

Abstract

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 He4 and Li7. 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 He4 abundances $Y_p$ = 0.225 -- 0.250, as well as a range in primordial Li7 abundances from (1.6 to 4.1) $ \times 10^{-10}$. For (Li7/H)$_p = 1.6 \times 10^{-10}$, as can be inferred from the Li7 data from Population II halo stars, the upper limit to $N_\nu$ based on the current best estimate of the primordial He4 abundance of $Y_p = 0.238$, is $N_\nu < 4.3$ and varies from $N_\nu < 3.3$ (at 95% C.L.) when $Y_p=0.225$ to $N_\nu < 5.3$ when $Y_p=0.250$. If Li7 is depleted in these stars the upper limit to $N_\nu$ is relaxed. Taking (Li7/H)$_p = 4.1 \times 10^{-10}$, the limit varies from $N_\nu < 3.9$ when $Y_p = 0.225$ to $N_\nu \la 6$ when $Y_p = 0.250$. We also consider the consequences on the upper limit to $N_\nu$ if recent observations of deuterium in high-redshift quasar absorption-line systems are confirmed.