Complementarity of peculiar velocity surveys and redshift space distortions for testing gravity
Alex Kim, Eric V. Linder
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 $f{\ensuremath{\sigma}}_{8}$ at $z\ensuremath{\lesssim}0.2$ where density tracers cannot do better than $\ensuremath{\sim}10%$. 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 $\ensuremath{\sigma}(\ensuremath{\gamma})\ensuremath{\approx}0.02$, 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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model assumption to a ${w}_{0}--{w}_{a}$ cosmology.