A Bayesian estimator for peculiar velocity correction in cosmological inference from supernovae data

ABSTRACT The peculiar motion of the host galaxies can shift the observed redshifts from their true values, introducing bias in estimating cosmological parameters from supernova data. The coherent component of peculiar motion is typically corrected using velocity-field reconstruction, while the random component is handled statistically by inflating the magnitude uncertainty through standard error propagation. However, velocity-field reconstruction requires assuming an underlying cosmology, which can bias the final inference, whereas the statistical treatment of the random component relies on a locally linear magnitude–redshift relation and a Gaussian velocity distribution. We present a Bayesian estimator for simultaneously correcting for peculiar motion while fitting a cosmological model to supernova data, relaxing the assumption of linearity of the model and Gaussianity of the peculiar motion. Our approach is based on considering the problem of fitting the magnitude–redshift relation as a non-linear model with errors in both dependent and independent variables. To this end, we develop a general method for fitting non-linear errors-in-variables models and apply it to the magnitude–redshift relation, validating it with simulated data sets at the precision of current and upcoming surveys and testing it on the pantheon sample. Our method provides an alternative approach for accounting for the peculiar velocity effects, which is a complementary method for the coherent component, as it does not require independent velocity measurements, and generalizes the treatment of the random component. Moreover, our general method is applicable to various other problems in cosmology and astronomy.