Complementarity of Peculiar Velocity Surveys and Redshift Space Distortions for Testing Gravity

Abstract

Peculiar-velocity surveys of the low-redshift universe have significant leverage to constrain the growth rate of cosmic structure and test gravity. Wide-field imaging surveys combined with multiobject spectrographs [e.g., ZTF2, Large Synoptic Survey Telescope (LSST), DESI, and 4MOST] can use type Ia supernovae as informative tracers of the velocity field, reaching few percent constraints on the growth rate f σ8 at z ≲0.2 where density tracers cannot do better than ∼10 %. Combining the high-redshift DESI survey mapping redshift space distortions with a low-redshift supernova peculiar velocity survey using LSST and DESI can determine the gravitational growth index to σ (γ )≈0.02 , testing general relativity. We study the characteristics needed for the peculiar velocity survey, and how its complementarity with clustering surveys improves when going from a Λ CDM model assumption to a w0- wa cosmology.