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

TL;DR

This paper introduces a Bayesian estimator that simultaneously corrects for peculiar velocities and fits cosmological models to supernova data, relaxing previous assumptions of linearity and Gaussianity.

Contribution

It develops a non-linear errors-in-variables model for supernova data, validated with simulations and the Pantheon sample, offering a flexible alternative to existing velocity correction methods.

Findings

Validated with simulated datasets at current and upcoming survey precision.

Tested on the Pantheon supernova sample.

Provides a non-linear, Gaussian-free correction method for peculiar velocities.

Abstract

The peculiar motion of the host galaxies introduces bias in estimating cosmological parameters from supernova data. The coherent component of the peculiar motion is usually corrected for using velocity field reconstruction based on the observed galaxy distribution, while the random component is treated statistically by inflating the magnitude uncertainty in the quadrature derived using the standard error propagation. The method of velocity field reconstruction requires assuming an underlying cosmology, which can introduce its own bias in the final inference. On the other hand, the statistical treatment of the random component assumes a locally linear approximation for the magnitude-redshift relation and a Gaussian distribution for the peculiar velocities, which can have extended tails in the non-linear regime. In this work, we present a Bayesian estimator for simultaneously correcting for peculiar motion while fitting a cosmological model to the supernova data, relaxing the assumption of linearity of the model and Gaussianity of the random 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 such non-linear errors-in-variables models. We then specialize it to the case of fitting the magnitude-redshift relation, validating it with simulated datasets 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.