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 today’s value, $G_0$, $G_{\mathrm{BBN}}/G_0={1.01}_{-0.16}^{+0.20}$ at the $68\%$ confidence level.

Figure 1

Observational limits and theoretical expectations for $\mathrm{D}/\mathrm{H}$ versus $\eta$. The $1\sigma$ (light shading) and $2\sigma$ (dark shading) observational uncertainties for $\mathrm{D}/\mathrm{H}$ and $\eta$ are shown. They do not appear as ellipses due to the linear scale in $\mathrm{D}/\mathrm{H}$ but logarithmic uncertainties from the observations. The BBN predictions are shown as the solid curves where the width is the $3\%$ theoretical uncertainties. Three different values of $G_{\mathrm{BBN}}/G_0$ are shown.