The current uncertainty in Newton’s constant $G_N$ is of the order of 0.15%. For values of the baryon to photon ratio consistent with both cosmic microwave background observations and the primordial deuterium abundance, this uncertainty in $G_N$ corresponds to an uncertainty in the primordial ${}^4\mathrm{He}$ mass fraction $Y_P$ of $\pm 1.3\times {10}^{-4}.$ This uncertainty in $Y_P$ is comparable to the effect from the current uncertainty in the neutron lifetime ${\tau }_n,$ which is often treated as the dominant uncertainty in calculations of $Y_P.$ Recent measurements of $G_N$ seem to be converging within a smaller range; a reduction in the estimated error on $G_N$ by a factor of 10 would essentially eliminate it as a source of uncertainty in the calculation of the primordial ${}^4\mathrm{He}$ abundance.

• Received 24 October 2003

DOI:https://doi.org/10.1103/PhysRevD.69.107302