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 BSBM theories considered here. 
J.D. Barrow, J. Magueijo and H.B. Sandvik