Measuring the Homogeneity of the Universe Using Polarization Drift
  We propose a method to probe the homogeneity of a general universe, without
assuming symmetry. We show that isotropy can be tested at remote locations on
the past lightcone by comparing the line-of-sight and transverse expansion
rates, using the time dependence of the polarization of Cosmic Microwave
Background photons that have been inverse-Compton scattered by the hot gas in
massive clusters of galaxies. This probes a combination of remote transverse
and parallel components of the expansion rate of the metric, and we may use
radial baryon acoustic oscillations or cosmic clocks to measure the parallel
expansion rate. Thus we can test remote isotropy, which is a key requirement of
a homogeneous universe. We provide explicit formulas that connect observables
and properties of the metric.
