4. NUCLEOSYNTHESIS

The observationally successful theory of the origin of the light elements by nucleosynthesis at redshift z ~ 10⁹ predicts the mean baryon density in terms of the primeval element abundances (as reviewed extensively in the literature; for example Walker et al. 1991, Copi et al. 1995, Hata et al. 1997). We consider here standard homogeneous nucleosynthesis predictions for abundances as a function of the baryon-to-photon ratio 10^-10 ₁₀, where the present baryon density is _baryonh₇₀² = 7.45 x 10^-3 ₁₀. In this context the strongest constraints on _baryon derive from the abundances of helium and deuterium.

The primordial deuterium abundance is still uncertain but we can quote reliable upper and lower bounds. A conservative lower bound, (D/H)_p 2 x 10^-5, comes from many sources - the Jovian atmosphere (e.g. Niemann 1996), the interstellar medium (Ferlet & Lemoine 1996, Linsky et al. 1995), and quasar absorption lines (Tytler, Fan & Burles 1996), together with the fact that no source outside the Big Bang is known to produce deuterium significantly. An upper bound, (D/H)_p 2 x 10^-4, comes from several measurements in metal-poor quasar absorption systems (Songaila et al. 1994; Carswell et al. 1994; Webb et al. 1997; Songalia, Wampler, & Cowie, 1997). Although the identification as deuterium in these systems is disputed (Tytler, Burles, & Kirkman 1997), the lack of higher detected values, and the fact that significant D destruction would normally be expected to produce significant metal enrichment, makes this a robust upper limit. These yield the limits 1.7 ₁₀ 7.2. The lower bound is used for the minimum value of _baryon in line 14 in Table 3. For comparison we include the central value favored by Burles and Tytler (1997), (D/H)_p = 3.4 x 10^-5, which yields ₁₀ = 5.1 or _baryon = 0.039h₇₀^-2.

The helium abundance Y is well measured in nearby galaxies (e.g., Pagel et al. 1992; Skillmann et al. 1994; Izotov, Thuan, & Lipovetsky 1997). The primordial value Y_p derived from these observations depends on models of stellar enrichment, but the present datasets yield a nearly model-independent 2 Bayesian upper limit Y_p 0.243 (Hogan, Olive, & Scully 1997). This corresponds to ₁₀ = 3.6, which we use for the maximum value in line 13 in Table 3; it is about half the upper limit from deuterium. Most current studies (e.g. Olive & Steigman 1995) are consistent with the central value Y_p 0.23 used in the table.