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 Yp derived from these observations depends on models of stellar enrichment, but the present datasets yield a nearly model-independent 2 Bayesian upper limit Yp 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 Yp 0.23 used in the table.