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, $\dot G/G \gg H$. 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.