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

TL;DR

This paper tackles biases in cosmological inferences from Type Ia supernovae introduced by host-galaxy peculiar motions. It introduces a Bayesian estimator that treats the magnitude–redshift relation as a nonlinear errors-in-variables problem, using latent true redshifts and magnitudes and a general posterior framework to jointly infer cosmological parameters while correcting for peculiar velocities. The method is validated on synthetic data and applied to the Pantheon SN sample, demonstrating robustness to both random and coherent velocity components and offering improvements over standard linear-Gaussian treatments, especially for future high-precision surveys. Beyond SN cosmology, the approach provides a versatile tool for nonlinear inference problems in cosmology and astronomy where measurement errors occur in both variables and model nonlinearity is important.

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.

Figures (6)

• Figure 1: Constraints on the $\Lambda$CDM parameters from synthetic data with magnitude error $\sigma_m = 0.2$ (left) and $\sigma_m = 0.05$ (right). Estimator $\mathcal{E}_1$ (red) ignores any contribution to redshift from the peculiar motion of supernovae host galaxies, $\mathcal{E}_2$ (blue) considers it for the linearized model (see Appendix \ref{['sec:A']} for details), while $\mathcal{E}_3$ (green) represents our estimator, which incorporates the contribution from peculiar motion for the exact model. The black dashed line represents the true values of the parameters. The errors on the estimated parameters are marginally larger for estimators $\mathcal{E}_2$ and $\mathcal{E}_3$.
• Figure 2: Constraints on the $w$CDM parameters from synthetic data with $\sigma_m = 0.2$ (left) and $\sigma_m = 0.05$ (right). The colour scheme of Figure \ref{['fig:LCDM_combined_syn']} is followed. The black dashed line represents the true values of the parameters. As in Figure \ref{['fig:LCDM_combined_syn']}, the errors on the estimated parameters are marginally larger for estimators $\mathcal{E}_2$ and $\mathcal{E}_3$. In addition, the analysis of synthetic data shows that the neglect of peculiar velocities might bias the estimation of cosmological parameters. The Figure in conjunction with Figure \ref{['fig:LCDM_combined_syn']} shows that this bias might not play an important role in the current data (left panel), but it would become important in the interpretation of the future data (right panel).
• Figure 3: Comparison of different estimators with only a random peculiar motion. The colour scheme of Figure \ref{['fig:LCDM_combined_syn']} is followed. Both $\mathcal{E}_2$ and $\mathcal{E}_3$ give similar results, and the standard estimator $\mathcal{E}_2$ is sufficient.
• Figure 4: Comparison of different estimators with only the coherent component of peculiar motion. The colour scheme of Figure \ref{['fig:LCDM_combined_syn']} is followed. As expected, $\mathcal{E}_2$ fails to capture the coherent component of peculiar motion, as it is constructed to handle the random contribution. It is therefore not directly comparable with $\mathcal{E}_3$ and is displayed with a dashed line. The estimator $\mathcal{E}_3$, however, correctly accounts for the coherent component.
• Figure 5: The figure shows posterior distributions and credible regions of $\Lambda$CDM parameters from Pantheon data using three different estimators. It follows the convention used in Figure \ref{['fig:LCDM_combined_syn']}. All the estimators give statistically consistent results.