Constraining spatial variations of the fine structure constant using
  clusters of galaxies and Planck data
  We propose an improved methodology to constrain spatial variations of the
fine structure constant using clusters of galaxies. We use the {\it Planck}
2013 data to measure the thermal Sunyaev-Zeldovich effect at the location of
618 X-ray selected clusters. We then use a Monte Carlo Markov Chain algorithm
to obtain the temperature of the Cosmic Microwave Background at the location of
each galaxy cluster. When fitting three different phenomenological
parameterizations allowing for monopole and dipole amplitudes in the value of
the fine structure constant we improve the results of earlier analysis
involving clusters and the CMB power spectrum, and we also found that the
best-fit direction of a hypothetical dipole is compatible with the direction of
other known anomalies. Although the constraining power of our current datasets
do not allow us to test the indications of a fine-structure constant dipole
obtained though high-resolution optical/UV spectroscopy, our results do
highlight that clusters of galaxies will be a very powerful tool to probe
fundamental physics at low redshift.
