Cosmological variation of the deuteron binding energy, strong interaction, and quark masses from big bang nucleosynthesis

We use big bang nucleosynthesis calculations and light element abundance data to constrain the relative variation of the deuteron binding energy since the Universe was a few minutes old, $\ensuremath{\delta}Q=Q(\mathrm{BBN})\ensuremath{-}Q(\mathrm{present}).$ Two approaches are used, first treating the baryon to photon ratio $\ensuremath{\eta}$ as a free parameter, but with the additional freedom of varying $\ensuremath{\delta}Q,$ and second using the WMAP value of $\ensuremath{\eta}$ and solving only for $\ensuremath{\delta}Q.$ Including varying Q yields a better fit to the observational data than imposing the present day value, rectifying the discrepancy between the ${}^{4}\mathrm{He}$ abundance and the deuterium and ${}^{7}\mathrm{Li}$ abundances, and yields good agreement with the independently determined ${\ensuremath{\eta}}_{\mathrm{WMAP}}.$ Using ${\ensuremath{\eta}}_{\mathrm{WMAP}},$ the minimal deviation consistent with the data is significant at about the $4\ensuremath{\sigma}$ level; $\ensuremath{\delta}Q/Q=\ensuremath{-}0.019\ifmmode\pm\else\textpm\fi{}0.005.$ If the primordial ${}^{4}\mathrm{He}$ abundance lies towards the low end of values in the literature, this deviation is even larger and more statistically significant. Taking the light element abundance data at face value, our result may be interpreted as variation of the dimensionless ratio ${X=m}_{s}/{\ensuremath{\Lambda}}_{\mathrm{QCD}}$ of the strange quark mass and strong scale: $\ensuremath{\delta}X/X=(1.1\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}.$ These results provide a strong motivation for a more thorough exploration of the potential systematic errors in the light element abundance data.