As just discussed in Section 4.6, there is some tension between the SBBN-predicted abundances of D and ^{4}He 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 ^{4}He 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 ^{4}He 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 ^{4}He 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 ^{7}Be 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} h^{2} = 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).