Measuring anisotropic stress with relativistic effects
  One of the main goal of large-scale structure surveys is to test the
consistency of General Relativity at cosmological scales. In the $\Lambda$CDM
model of cosmology, the relations between the fields describing the geometry
and the content of our Universe are uniquely determined. In particular, the two
gravitational potentials -- that describe the spatial and temporal fluctuations
in the geometry -- are equal. Whereas large classes of dark energy models
preserve this equality, theories of modified gravity generally create a
difference between the potentials, known as anisotropic stress. Even though
measuring this anisotropic stress is one of the key goals of large-scale
structure surveys, there are currently no methods able to measure it directly.
Current methods all rely on measurements of galaxy peculiar velocities (through
redshift-space distortions), from which the time component of the metric is
inferred, assuming that dark matter follows geodesics. If this is not the case,
all the proposed tests fail to measure the anisotropic stress. In this letter,
we propose a novel test which directly measures anisotropic stress, without
relying on any assumption about the unknown dark matter. Our method uses
relativistic effects in the galaxy number counts to provide a direct
measurement of the time component of the metric. By comparing this with lensing
observations our test provides a direct measurement of the anisotropic stress.
