Principal component analysis of modified gravity using weak lensing and peculiar velocity measurements

Abstract

We perform a principal component analysis to assess ability of futureobservations to measure departures from General Relativity inpredictions of the Poisson and anisotropy equations on linearscales. In particular, we focus on how the measurements ofredshift-space distortions (RSD) observed from spectroscopic galaxyredshift surveys will improve the constraints when combined withlensing tomographic surveys. Assuming a Euclid-like galaxy imaging andredshift survey, we find that adding the 3D information decreases thestatistical uncertainty by a factor between 3 and 7 compared to thecase when only observables from lensing tomographic surveys areused. We also find that the number of well-constrained modes increasesby a factor between 3 and 6. Our study indicates the importance ofjoint galaxy imaging and redshift surveys such as SuMIRe and Euclid togive more stringent tests of the ΛCDM model and to distinguishbetween various modified gravity and dark energy models.