Deriving accurate peculiar velocities (even at high redshift)

The way that peculiar velocities are often inferred from measurements of distances and redshifts makes an approximation, vp = cz − H0D, that gives significant errors even at relatively low redshifts (overestimates by Δvp ∼ 100 km s−1 at z ∼ 0.04). Here, we demonstrate where the approximation breaks down, the systematic offset it introduces, and how the exact calculation should be implemented.