Principal Component Analysis of Modified Gravity using Weak Lensing and Peculiar Velocity Measurements

TL;DR

This paper uses principal component analysis to evaluate how future combined weak lensing and peculiar velocity measurements can improve constraints on deviations from General Relativity on linear scales.

Contribution

It demonstrates that combining spectroscopic galaxy redshift surveys with lensing surveys significantly enhances the ability to detect modifications to gravity.

Findings

Adding 3D RSD data reduces uncertainty by a factor of 3-10.

Number of well-constrained modes increases by 3-7 times.

Joint surveys like Euclid improve tests of the DM model.

Abstract

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.