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 α in time (or redshift) cannot occur in Friedmann universes in the Bekenstein-Sandvik-Barrow-Magueijo theories considered here.