The role of peculiar velocity uncertainties in standard siren cosmology

Local distance indicators such as standard sirens, in combination with spectroscopic redshift measurements of their host galaxies, allow us to estimate the present-day expansion rate of the Universe parameterised by Hubble’s constant, H_0. However, these observed redshifts are systematically modified by the effect of galaxy peculiar velocities. Although these velocities may be estimated from the local density field by the process of velocity-field reconstruction, the intrinsic errors and covariance in these estimates contribute to the error in the H_0 determination. In this paper we demonstrate how the impact of peculiar velocities can be propagated into H_0 measurements from local distance indicators with observed redshifts, incorporating the full covariance of the velocity field induced by bulk flows. We apply our methods to cosmological simulations, testing the importance of this effect in the context of future analyses of gravitational wave sources with electromagnetic counterparts used as bright sirens. We conclude that H_0 errors may be increased by a factor of 2 in comparison with neglecting peculiar velocity covariance, for GW170817-like sirens located within 50 Mpc with 5% distance errors, with the highest impacts expected for sources at nearby distances or with small distance errors. Our analytical methods may also be applied to other local distance indicators, such as Type Ia supernovae.