Abstract
We study inhomogeneous cosmological variations in the fine structure `'constant'' $\ensuremath{\alpha}$ in Friedmann universes. Inhomogeneous motions of the scalar field driving changes in $\ensuremath{\alpha}$ 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 \ensuremath{\alpha} in time (or redshift) cannot occur in Friedmann universes in the Bekenstein-Sandvik-Barrow-Magueijo theories considered here.
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