5.3. The Nucleosynthesis Check
The central density in equation (38) with h70 = 1 corresponds to 10 = 2.8. At this value of the baryon-to-photon ratio the standard model for light element nucleosynthesis predicts Yp(4He) 0.238 and D/H 9 x 10-5. This is consistent with observations of the helium abundance, if somewhat above the central value, and with current observations of the deuterium abundance, if somewhat toward the high end of the range of estimates (Songaila 1997). The mean of the upper limit from helium and the lower limit from deuterium is 10 = 2.7 which we adopt as the central value in line 14 of Table 3.
If the baryon density were at the low end of our range of estimates in line 8 in Table 3, baryon = 0.007 (10 = 1.0 at h70 = 1), the standard model prediction for the deuterium abundance would be unacceptably large. This could be remedied by assuming a significant baryon mass has been sequestered in the MACHOs, but for the reasons explained above we are inclined to suspect rather that the adopted minima in lines 7a and 7b in Table 3 seriously underestimate the mass in plasma. The baryon density at the high end of our estimates is baryon = 0.041 (10 = 5.5 at h70 = 1). This density is consistent with the bound from the deuterium abundance but it predicts Yp = 0.247, well outside the accepted bound on the primeval helium mass fraction. In our opinion the likely interpretation is that our upper limit in line 8 of Table 3 also is overly conservative.
Our interpretation of the baryon budget assumes the standard homogeneous model for primordial nucleosynthesis. An inhomogeneous primeval entropy per baryon, with the appropriate coherence length (Jedamzik & Fuller 1995), would require serious attention if further observations confirmed that there are significant variations in the deuterium abundances in high redshift HI clouds or that the helium abundances in some dwarf galaxies are lower than that predicted by the global baryon budget applied to the homogeneous nucleosynthesis model.