Measuring the distortion of time with relativistic effects in
  large-scale structure
  To test the theory of gravity one needs to test, on one hand, how space and
time are distorted by matter and, on the other hand, how matter moves in a
distorted space-time. Current observations provide tight constraints on the
motion of matter, through the so-called redshift-space distortions, but they
only provide a measurement of the sum of the spatial and temporal distortions,
via gravitational lensing. In this Letter, we develop a method to measure the
time distortion on its own. We show that the coming generation of galaxy
surveys, like the Square Kilometer Array, will allow us to measure the
distortion of time with an accuracy of 10-30\%. Such a measurement will be
essential to test deviations from General Relativity in a fully
model-independent way. In particular, it can be used to compare the spatial and
temporal distortions of space-time, that are predicted to be the same in
$\Lambda$CDM but generically differ in modified theories of gravity.
