Testing General Relativity with the Doppler magnification effect
  The apparent sizes and brightnesses of galaxies are correlated in a dipolar
pattern around matter overdensities in redshift space, appearing larger on
their near side and smaller on their far side. The opposite effect occurs for
galaxies around an underdense region. These patterns of apparent magnification
induce dipole and higher multipole terms in the cross-correlation of galaxy
number density fluctuations with galaxy size/brightness (which is sensitive to
the convergence field). This provides a means of directly measuring peculiar
velocity statistics at low and intermediate redshift, with several advantages
for performing cosmological tests of GR. In particular, it does not depend on
empirically-calibrated scaling relations like the Tully-Fisher and Fundamental
Plane methods. We show that the next generation of spectroscopic galaxy
redshift surveys will be able to measure the Doppler magnification effect with
sufficient signal-to-noise to test GR on large scales. We illustrate this with
forecasts for the constraints that can be achieved on parametrised deviations
from GR for forthcoming low-redshift galaxy surveys with DESI and SKA2.
Although the cross-correlation statistic considered has a lower signal to noise
than RSD, it will be a useful probe of GR since it is sensitive to different
systematics.
