Primordial nucleosynthesis with a varying fine structure constant: An improved estimate

We compute primordial light-element abundances for cases with a fine structure constant $\alpha$ different from the present value, including many sources of $\alpha$ dependence neglected in previous calculations. Specifically, we consider contributions arising from Coulomb barrier penetration, photon coupling to nuclear currents, and the electromagnetic components of nuclear masses. We find the primordial abundances to depend more weakly on $\alpha$ than previously estimated, by up to a factor of 2 in the case of ${}^7\mathrm{Li}.$ We discuss the constraints on variations in $\alpha$ from the individual abundance measurements and the uncertainties affecting these constraints. While the present best measurements of primordial D/H, ${}^4\mathrm{He}/\mathrm{H},$ and ${}^7\mathrm{Li}/\mathrm{H}$ may be reconciled pairwise by adjusting $\alpha$ and the universal baryon density, no value of $\alpha$ allows all three to be accommodated simultaneously without consideration of systematic error. The combination of measured abundances with observations of acoustic peaks in the cosmic microwave background favors no change in $\alpha$ within the uncertainties.