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

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 multi-object spectrographs (e.g. ZTF2, LSST, DESI, 4MOST) can use Type Ia supernovae as informative tracers of the velocity field, reaching few percent constraints on the growth rate $fσ_8$ at $z\lesssim0.2$ where density tracers cannot do better than $\sim10\%$. 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 $σ(γ)\approx0.02$, 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 $w_0$-$w_a$ cosmology.

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