SIMBAD references

We analyze the effect that peculiar velocities have on the cosmological inferences we make using luminosity distance indicators, such as Type Ia supernovae. In particular we study the corrections required to account for (1) our own motion, (2) correlations in galaxy motions, and (3) a possible local under- or overdensity. For all of these effects we present a case study showing the impact on the cosmology derived by the Sloan Digital Sky Survey-II Supernova Survey (SDSS-II SN Survey). Correcting supernova (SN) redshifts for the cosmic microwave background (CMB) dipole slightly overcorrects nearby SNe that share some of our local motion. We show that while neglecting the CMB dipole would cause a shift in the derived equation of state of Δw ∼ 0.04 (at fixed Ω_m), the additional local-motion correction is currently negligible (Δw ≲ 0.01). We then demonstrate a covariance-matrix approach to statistically account for correlated peculiar velocities. This down-weights nearby SNe and effectively acts as a graduated version of the usual sharp low-redshift cut. Neglecting coherent velocities in the current sample causes a systematic shift of Δw ∼ 0.02. This will therefore have to be considered carefully when future surveys aim for percent-level accuracy and we recommend our statistical approach to down-weighting peculiar velocities as a more robust option than a sharp low-redshift cut.