A New Nucleosynthesis Constraint on the Variation of G

Abstract

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, $G_0$, $G_{BBN}/G_0=1.01^{+0.20}_{-0.16}$ 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 $-0.004 < \alpha < 0.005$. This would translate into $-3\times10^{-13} \textrm{yr}^{-1} < (\dot G/G)_{\textrm{today}} < 4 \times 10^{-13} \textrm{yr}^{-1}$.