Assessing Big-Bang nucleosynthesis.

Systematic uncertainties in the light-element abundances and their evolution make a rigorous statistical assessment difficult. However, using Bayesian methods we show that the following statement is robust: the predicted and measured abundances are consistent with 95% credibility only if the baryon-to-photon ratio is between 2× 10 and 6.5× 10 and the number of light neutrino species is less than 3.9. Our analysis suggests that the He abundance may have been systematically underestimated. Big-bang nucleosynthesis occurred seconds after the bang and for this reason offers the most stringent test of the standard cosmology. Comparison of the predicted and measured light-element abundances has evolved dramatically over the past thirty years, beginning with the observation that there was evidence for a significant primeval abundance of He which could be explained by the big bang [16] to the present where the abundances of D, He, He and Li are all used to test the big bang. The predictions of big-bang nucleosynthesis depend upon the baryon-to-photon ratio (≡ η) as well as the number of light (< ∼ 1MeV) particle species, often quantified as the equivalent number of massless neutrino species (≡ Nν). For a decade it has been argued that the abundances of all four light elements can be accounted for provided η is between 2.5× 10 and 6× 10 and Nν < 3.1− 4 [17, 18, 19]. The “consistency interval” provides the best determination of the baryon density and is key to the case for the existence of nonbaryonic dark matter. The limit to Nν provides a crucial hurdle for theories that aspire to unify the fundamental forces and particles. However, these conclusions were not based upon a rigorous statistical analysis. Because the dominant uncertainties in the light-element abundances are systematic such an analysis is difficult and previous work focussed on concordance intervals. Given the importance of big-bang nucleosynthesis it is worthwhile to try to use more rigorous methods. Here we apply two standard methods, goodness of fit and Bayesian likelihood, and identify the the conclusions which are insensitive to the systematic errors. We begin by reviewing the general situation. The predictions of standard big-bang nucleosynthesis are shown in Fig. 1. The theoretical uncertainties are statistical, arising from imprecise knowledge of the neutron lifetime and certain nuclear cross sections. Because of 10 Gyr or so of “chemical evolution” since the big bang (nuclear reactions in stars and elsewhere which modify the light-element abundances) determining primeval abundances is not simple and the dominant uncertainties are systematic. The chemical evolution of He is straightforward: stars make additional He. Stars also make metals (elements heavier than He); by measuring the He abundance in metal-poor, extragalactic HII (ionized hydrogen) clouds as a function of some metal indicator (e.g., C, N or O) and extrapolating to zero metallicity a primeval abundance has been inferred: YP = 0.232 ± 0.003 (stat) ± 0.005 (sys) [20]. Systematic uncertainties arise from trying to convert line strengths to abundances by modeling. The range YP = 0.221 − 0.243 allows for 2σ statistical + 1σ systematic uncertainty and is consistent with the big-bang prediction provided η ≃ (0.8− 4)× 10 [17]. Others have argued that the systematic uncertainty is a factor of two or even three larger [21]; taking YP ≃ 0.21− 0.25 increases the concordance range significantly, η ≃ (0.6− 10)× 10, reflecting the logarithmic dependence of big-bang He production upon η [17]. There is a strong case that the Li abundance measured in metal-poor, old pop II halo stars, Li/H = (1.5 ± 0.3) × 10, reflects the big-bang abundance [22]. However, it is possible that even in these stars the Li abundance has been reduced by nuclear burning, perhaps by a factor of two (the presence of Li in some of these stars, which is more fragile, provides an upper limit to the amount of astration). Allowing for a 2σ statistical uncertainty