Variations of alpha in space and time

We study inhomogeneous cosmological variations in the fine structure ''constant" alpha in Friedmann universes. Inhomogeneous motions of the scalar field driving changes in alpha display spatial oscillations that decrease in amplitude with increasing time. The inhomogeneous evolution quickly approaches that found for exact Friedmann universes. We prove a theorem to show that oscillations of alpha in time (or redshift) cannot occur in Friedmann universes in the Bekenstein-Sandvik-Barrow-Magueijo theories considered here.