Early-universe constraints on a time-varying fine structure constant

Recent high-resolution CMB anisotropy data seem to point to a value for the baryon density larger than the one preferred by Standard Big Bang Nucleosynthesis, ruling out a large set of {\it standard} cosmological models. However, present CMB data can be made compatible with a lower value for the baryon density if the fine-structure constant $\alpha$ was smaller in the past. In this letter we produce early-universe constraints on a time-varying $\alpha$ by a joint analysis of the latest CMB and BBN data. We find strong constraints on the variation of $\alpha$ from BBN, $\Delta \alpha / \alpha =(-7 \pm 5) 10^{-3}$ (68% C.L.), marginally compatible with the CMB result, $\Delta \alpha / \alpha =-0.10 \pm 0.05$ (68% C.L.). We conclude that the varying $\alpha$ scenario may still solve the CMB-BBN discrepancy, but that may require a non-monotonic red-shift behaviour for the fine structure constant