We study the impact on the primordial abundances of light elements created by a variation of the quark masses at the time of Big Bang nucleosynthesis (BBN). In order to navigate through the particle and nuclear physics required to connect quark masses to binding energies and reaction rates in a model-independent way, we use lattice QCD data and a hierarchy of effective field theories. We find that the measured ${}^4\mathrm{He}$ abundances put a bound of $-1\%\lesssim \delta m_q/m_q\lesssim 0.7\%$ on a possible variation of quark masses. The effect of quark mass variations on the deuterium abundances can be largely compensated by changes of the baryon-to-photon ratio $\eta$. Including bounds on the variation of $\eta$ coming from WMAP results and adding some additional assumptions further narrows the range of allowed values of $\delta m_q/m_q$.

• Received 22 December 2010

DOI:https://doi.org/10.1103/PhysRevC.83.045803