Big bang nucleosynthesis with rapidly varying G

We examine big bang nucleosynthesis (BBN) in models with a time-varying gravitational constant G, when this time variation is rapid on the scale of the expansion rate H, i. e, G/G. Such models can arise naturally in the context of scalar-tensor theories of gravity and result in additional terms in the Friedman equation. We examine two representative models: a step-function evolution for G and a rapidly oscillating G. In the former case, the additional terms in the Friedman equation tend to cancel the effects of an initial value of G that differs from the present-day value. In the case of deuterium, this effect is large enough to reverse the sign of the change in (D/H) for a given change in the initial value of G. For rapidly oscillating G, the effect on the Friedman equation is similar to that of adding a vacuum energy density, and BBN allows upper limits to be placed on the product of the oscillation frequency and amplitude. The possibility that a rapidly oscillating G could mimic a cosmological constant is briefly discussed.