5. BBN IN NON-STANDARD MODELS

As just discussed in Section 4.6, there is some tension between the SBBN-predicted abundances of D and ⁴He and their primordial abundances inferred from current observational data (see Fig. 13). Another way to see the challenge is to superpose the data on the BBN predictions from Figure 2, where the Y_P versus D/H relations are shown for several values of N (SSG). This is done in Figure 15 where it is clear that the data prefer nonstandard BBN, with N closer to 2 than to the standard model value of 3.

Figure 15. The BBN-predicted primordial 4He mass fraction Y as a function of the BBN-predicted primordial Deuterium abundance (by number relative to Hydrogen) for three choices of N. Also shown by the filled circle and error bars are the primordial abundances adopted here (Section 4).

It is easy to understand this result on the basis of the earlier discussion (see Section 2.3). The adopted abundance of D serves, mainly, to fix the baryon density which, in turn, determines the SBBN-predicted ⁴He abundance. The corresponding predicted value of Y_P is too large when compared to the data. A universe which expands more slowly (S < 1; N < 3) will permit more neutrons to transmute into protons before BBN commences, resulting in a smaller ⁴He mass fraction. However, there are two problems (at least!) with this "solution". The main issue is that there are three "flavors" of light neutrinos, so that N 3 ( N 0). The second, probably less serious problem is that a slower expansion permits an increase in the ⁷Be production, resulting in an increase in the predicted relic abundance of lithium. For (D/H)_P = 3.0 × 10^-5 and Y_P = 0.238, the best fit values of and N are: ₁₀ = 5.3 (_B h² = 0.019) and N = 2.3 ( N = -0.7). For this combination the BBN-predicted lithium abundance is [Li]_P = 2.53 ((Li/H)_P = 3.4 × 10^-10), somewhat higher than, but still in agreement with the PSWN estimate of [Li]_P = 2.4 ± 0.2, but much higher than the RBOFN value of [Li]_P = 2.1 ± 0.1. Although the tension between the observed and SBBN-predicted lithium abundances may not represent a serious challenge (at present), the suggestion that N < 0 must be addressed. One possibility is that the slower expansion of the radiation-domianted early universe could result from a non-minimally coupled scalar field ("extended quintessence") whose effect is to change the effective gravitational constant (G G' < G; see Section 2.3). For a discussion of such models and for further references see, e.g. Chen, Scherrer & Steigman (2001).