2.2. The SBBN-Predicted Abundances
The primordial abundances of D, 3He, and 7Li(7Be) are rate limited, depending sensitively on the competition between the nuclear reactions rates and the universal expansion rate. As a result, these nuclides are potential baryometers since their abundances are sensitive to the universal density of nucleons. As the universe expands, the nucleon density decreases so it is useful to compare the nucleon density to that of the CMB photons nN / n. Since this ratio will turn out to be very small, it is convenient to introduce
As the universe evolves (post-e± annihilation) this ratio is accurately preserved so that BBN = 0. Testing this relation over ten orders of magnitude in redshift, over a range of some ten billion years, can provide a confirmation of or a challenge to the standard model.
In contrast to the other light nuclides, the primordial abundance of 4He (mass fraction Y) is relatively insensitive to the baryon density, but since virtually all neutrons available at BBN are incorporated in 4He, it does depend on the competition between the weak interaction rate (largely fixed by the accurately measured neutron lifetime) and the universal expansion rate (which depends on geff). The higher the nucleon density, the earlier can the D-bottleneck be breached. At early times there are more neutrons and, therefore, more 4He will be synthesized. This latter effect is responsible for the very slow (logarithmic) increase in Y with . Given the standard model relation between time and temperature and the nuclear and weak cross sections and decay rates measured in the laboratory, the evolution of the light nuclide abundances may be calculated and the frozen-out relic abundances predicted as a function of the one free parameter, the nucleon density or . These are shown in Figure 1.
Figure 1. The SBBN-predicted primordial abundances of D, 3He, 7Li (by number with respect to hydrogen), and the 4He mass fraction Y as a function of the nucleon abundance 10. The widths of the bands reflect the theoretical uncertainties.
Not shown on Figure 1 are the relic abundances of 6Li, 9Be, 10B, and 11B, all of which, over the same range in , lie offscale, in the range 10-20 - 10-13.
The reader may notice the abundances appear in Figure 1 as bands. These represent the theoretical uncertainties in the predicted abundances. For D/H and 3He/H they are at the ~ 8% level, while they are much larger, ~ 12%, for 7Li. The reader may not notice that a band is also shown for 4He, since the uncertainty in Y is only at the ~ 0.2% level (Y 0.0005). The results shown here are from the BBN code developed and refined over the years by my colleagues at The Ohio State University. They are in excellent agreement with the published results of the Chicago group (Burles, Nollett & Turner 2001) who, in a reanalysis of the relevant published cross sections have reduced the theoretical errors by roughly a factor of three for D and 3He and a factor of two for 7Li. The uncertainty in Y is largely due to the (very small) uncertainty in the neutron lifetime.
The trends shown in Figure 1 are easy to understand based on our previous discussion. D and 3He are burned to 4He. The higher the nucleon density, the faster this occurs, leaving behind fewer nuclei of D or 3He. The very slight increase of Y with is largely due to BBN starting earlier, at higher nucleon density (more complete burning of D, 3H, and 3He to 4He) and neutron-to-proton ratio (more neutrons, more 4He). The behavior of 7Li is more interesting. At relatively low values of 3, mass-7 is largely synthesized as 7Li (by 3H(, ) 7Li reactions) which is easily destroyed in collisons with protons. So, as increases at low values, 7Li/H decreases. However, at relatively high values of 3, mass-7 is largely synthesized as 7Be (via 3He(, ) 7Be reactions) which is more tightly bound than 7Li and, therefore, harder to destroy. As increases at high values, the abundance of 7Be increases. Later in the evolution of the universe, when it is cooler and neutral atoms begin to form, 7Be will capture an electron and -decay to 7Li.