Principal Component Analysis of Modified Gravity using Weak Lensing and
  Peculiar Velocity Measurements
  We perform a principal component analysis to assess ability of future
observations to measure departures from General Relativity in predictions of
the Poisson and anisotropy equations on linear scales. In particular, we focus
on how the measurements of redshift-space distortions (RSD) observed from
spectroscopic galaxy redshift surveys will improve the constraints when
combined with lensing tomographic surveys. Assuming a Euclid-like galaxy
imaging and redshift survey, we find that adding the 3D information decreases
the statistical uncertainty by a factor between 3 and 10 compared to the case
when only observables from lensing tomographic surveys are used. We also find
that the number of well-constrained modes increases by a factor between 3 and
7. Our study indicates the importance of joint galaxy imaging and redshift
surveys such as SuMIRe and Euclid to give more stringent tests of the
{\Lambda}CDM model and to distinguish between various modified gravity and dark
energy models.
