Constraints on Spatial Variations in the Fine-Structure constant from
  Planck
  We use the Cosmic Microwave Background (CMB) anisotropy data from Planck to
constrain the spatial fluctuations of the fine-structure constant \alpha.
Through Thompson scattering of CMB photons, spatial anisotropies of \alpha lead
to higher-order correlations in the CMB anisotropies. We use a quadratic
estimator based on the four-point correlation function of the CMB temperature
anisotropy to extract the angular power spectrum of the spatial variation of
the fine-structure constant projected along the line of sight at the last
scattering surface. At tens of degree angular scales and above, we constrain
the rms fluctuations of the fine structure constant to be \delta
\alpha/\alpha_0= (1.34 +/- 5.82) x 10^-2 at the 95% confidence level with
respect to the standard value \alpha_0. We find no evidence for a spatially
varying \alpha at a redshift of 10^3.
