Higher-dimensional theories have the remarkable feature of predicting a tim
e (and hence redshift) dependence of the "fundamental" four dimensional con
stants on cosmological time scales. In this paper, we update the bounds on
a possible variation of the fine structure constant a at the time of big ba
ng nucleosynthesis (z similar to 10(10)) and cosmic microwave background (C
MB) (z similar to 10(3)). Using the recently released high-resolution CMB a
nisotropy data and the, latest estimates of primordial abundances of He-4 a
nd D, we do not find evidence for a varying alpha at more than a one sigma
level at either epoch.