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Higher-dimensional theories have the remarkable feature of predicting a time (and hence redshift) dependence of the ``fundamental'' four dimensional constants on cosmological time scales. In this paper, we update the bounds on a possible variation of the fine structure constant at the time of big bang nucleosynthesis (z10^10) and cosmic microwave background (CMB) (z10^3). 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 at more than a one-sigma level at either epoch.
Avelino et al. (Tue,) studied this question.