Improved BBN Constraints on the Variation of the Gravitational Constant

Abstract: Big Bang Nucleosynthesis (BBN) is very sensitive to the cosmological expansion rate. If the gravitational constant $G$ took a different value during the nucleosynthesis epoch than today, the primordial abundances of light elements would be affected. In this work, we improve the bounds on this variation using recent determinations of the primordial element abundances, updated nuclear and weak reaction rates and observations of the Cosmic Microwave Background (CMB). When combining the measured abundances and the baryon density from CMB observations by Planck, we find $G_\mathrm{BBN}/G_0 = 0.99^{+0.06}_{-0.05}$ at $2\sigma$ confidence level. If the variation of $G$ is linear in time, we find $\dot{G}/G_0 = 0.7^{+3.8}_{-4.3}\times 10^{-12} \, \mathrm{yr}^{-1}$, again at $2\sigma$. These bounds are significantly stronger than those from previous primordial nucleosynthesis studies, and are comparable and complementary to CMB, stellar, solar system, lunar laser ranging, pulsar timing and gravitational wave constraints.