The relic abundances of D, 3He, and 7Li are rate limited, determined by the competition between the early Universe expansion rate and the nucleon density. Any of these three nuclides is, therefore, a potential baryometer; see Figure 1.
Figure 1. The SBBN-predicted abundances of D, 3He, and 7Li by number with respect to hydrogen, and the 4He mass fraction YP, as a function of the nucleon (baryon) abundance parameter 10. The bands reflect the theoretical uncertainties ( ± 1) in the BBN predictions.
In contrast to the synthesis of the other light nuclides, once BBN begins (T 80 keV) the reactions building 4He are so rapid that its relic abundance is not rate limited. The primordial abundance of 4He is limited by the availability of neutrons. To a very good approximation, its relic abundance is set by the neutron abundance at the beginning of BBN. As a result, the primordial mass fraction of 4He, YP, while being a relatively insensitive baryometer (see Figure 1), is an excellent, early-Universe chronometer.
The qualitative effects of a nonstandard expansion rate on the relic abundances of the light nuclides may be understood with reference to Figure 1. For the baryon abundance range of interest the relic abundances of D and 3He are decreasing functions of ; in this range, D and 3He are being destroyed to build 4He. A faster than standard expansion (S > 1) provides less time for this destruction so that more D and 3He will survive. The same behavior occurs for 7Li at low values of , where its abundance is a decreasing function of . However, at higher values of , the BBN-predicted 7Li abundance increases with , so that less time available results in less production and a smaller 7Li relic abundance. Except for dramatic changes to the early-Universe expansion rate, these effects on the relic abundances of D, 3He, and 7Li are subdominant to their variations with the baryon density. Not so for 4He, whose relic abundance is very weakly (logarithmically) dependent on the baryon density, but very strongly dependent on the early-Universe expansion rate. A faster expansion leaves more neutrons available to build 4He; to a good approximation Y 0.16 (S - 1). It is clear then that if 4He is paired with any of the other light nuclides, together they can constrain the baryon density ( or B h2 B) and the early-Universe expansion rate (S or N).
As noted above in Section 2, the neutron-proton ratio at BBN can also be modified from its standard value in the presence of a significant electron-neutrino asymmetry (e 0.01). As a result, YP is also sensitive to any neutrino asymmetry. More e than e drives the neutron-to-proton ratio down (see Eq. 1), leaving fewer neutrons available to build 4He; to a good approximation Y -0.23 e (Kneller & Steigman 2003). In contrast, the relic abundances of D, 3He, and 7Li are very insensitive to e 0, so that when paired with 4He, they can simultaneously constrain the baryon density and the electron-neutrino asymmetry. Notice that if both S and e are allowed to be free parameters, another observational constraint is needed to simultaneously constrain , S, and e. While neither 3He nor 7Li can provide the needed constraint, the CBR temperature anisotropy spectrum, which is sensitive to and S, but not to e, can (see Barger et al. 2003b). This review will concentrate on combining constraints from the CBR and SBBN (S = 1, e = 0) and also for S 1 (e = 0). For the influence of and constraints on electron neutrino asymmetry, see [Barger et al. (2003b)] and further references therein.