A New Nucleosynthesis Constraint on the Variation of G

Big Bang Nucleosynthesis can provide, via constraints on the expansion rate at that time, limits on possible variations in Newton’s Constant, $G$. The original analyses were performed before an independent measurement of the baryon-to-photon ratio from the cosmic microwave background was available. Combining this with recent measurements of the primordial deuterium abundance in quasar absorption systems now allows one to derive a new tighter constraint on $G$ without recourse to considerations of helium or lithium abundances. We find that, compared to todays value, $G_0$, $G_{BBN}\mathrm{/}{G}_0=1.01_{-0.16}^{+0.20}$ at the 68.3% confidence level. If we assume a monotonic power law time dependence, $G\propto t^{-\alpha }$, then the constraint on the index is $-0.004 < \alpha < 0.005$\mathrm{.}Thiswouldtranslateinto$-3\times10^{-13} $\text{yr}$^{-1} < (\dot G/G)_{$\text{today}$} < 4 \times 10^{-13} $\text{yr}$^{-1}$.