The local galaxy peculiar velocity field can be reconstructed from the
surrounding distribution of large-scale structure and plays an important role
in calibrating cosmic growth and expansion measurements. In this paper, we
investigate the effect of the stochasticity of these velocity reconstructions
on the statistical and systematic errors in cosmological inferences. By
introducing a simple statistical model between the measured and theoretical
velocities, whose terms we calibrate from linear theory, we derive the bias in
the model velocity. We then use lognormal realisations to explore the potential
impact of this bias when using a cosmic flow model to measure the growth rate
of structure, and to sharpen expansion rate measurements from host galaxies for
gravitational wave standard sirens with electromagnetic counterparts. Although
our illustrative study does not contain fully realistic observational effects,
we demonstrate that in some scenarios these corrections are significant and
result in a measurable improvement in determinations of the Hubble constant
compared to standard forecasts.Comment: 10 pages, 10 figures, 1 table, 1 appendix. Submitted to MNRAS.
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