  We study the effects on cosmic microwave background (CMB) temperature and
polarization anisotropies of spatial fluctuations of the fine-structure
parameter between causally disconnected regions of the Universe at the time of
recombination. Analogous to weak gravitational lensing, in addition to
modifying the mean power spectra and inducing a curl component (B mode) to the
polarization, spatial fluctuations of the fine-structure parameter induce
higher-order (non-Gaussian) temperature and polarization correlations in the
CMB. We calculate these effects for the general case of arbitrary correlation
between temperature fluctuations and fine-structure parameter fluctuations, and
show the results for a model where these two types of fluctuations are
uncorrelated. The formalism we present here may also be applied to other
modifications of recombination physics that do not significantly alter the
evolution of the dominant density perturbations. We discuss the constraints on
the effective Lagrangian for variable fine-structure parameter necessary to
realize this scenario.
