2.3. Variations On A Theme: Non-Standard BBN

Before moving on, let's take a diversion to which we'll return again in Section 5. Suppose the standard model is modified through the addition of extra relativistic particles ( N > 0; SSG). Equivalently (ignoring some small differences), it could be that the gravitational constant in the early universe differs from its present value (G G' G). Depending on whether G' > G or G' < G, the early universe expansion rate can be speeded up or slowed down compared to the standard rate. For concreteness, let's assume that S > 1. Now, there will be less time to destroy D and ³He, so their relic abundances will increase relative to the SBBN prediction. There is less time for neutrons to transform to protons. With more neutrons available, more ⁴He will be synthesized. The changes in ⁷Li are more complex. At low there is less time to destroy ⁷Li, so the relic ⁷Li abundance increases. At high there is less time to produce ⁷Be, so the relic ⁷Li (mass-7) abundance decreases.

Since the ⁴He mass fraction is relatively insensitive to the baryon density, it provides an excellent probe of any changes in the expansion rate. The faster the universe expands, the less time for neutrons to convert to protons, the more ⁴He will be synthesized. The increase in Y for "modest" changes in S is roughly Y 0.16(S - 1) 0.013 N. In Figure 2 are shown the BBN-predicted Y versus the BBN-predicted Deuterium abundance (relative to Hydrogen) for three choices of N (N 3 + N).

Figure 2. 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. The width of the bands represents the theoretical uncertainty, largely due to that of the neutron lifetime n.