Time drift of cosmological redshifts as a test of the Copernican   principle
  We present the time drift of the cosmological redshift in a general spherically symmetric spacetime. We demonstrate that its observation would allow us to test the Copernican principle and so determine if our universe is radially inhomogeneous, an important issue in our understanding of dark energy. In particular, when combined with distance data, this extra observable allows one to fully reconstruct the geometry of a spacetime describing a spherically symmetric under-dense region around us, purely from background observations. 
Jean-Philippe Uzan, Chris Clarkson, and George F.R. Ellis