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

Higher-dimensional theories have the remarkable feature of predicting a time (and hence redshift) dependence of the `fundamental' four dimensional constants on cosmological timescales. In this paper we update the bounds on a possible variation of the fine structure constant alpha at the time of BBN (z =10^10) and CMB (z=10^3). Using the recently-released high-resolution CMB anisotropy data and the latest estimates of primordial abundances of 4He and D, we do not find evidence for a varying alpha at more than one-sigma level at either epoch.