Quantifying concordance of correlated cosmological data sets

TL;DR

This paper introduces statistically optimal estimators to quantify agreement or disagreement between correlated cosmological data sets, accounting for data correlations and non-Gaussianities, and demonstrates their application to supernovae measurements of the Hubble constant.

Contribution

It develops new estimators for data concordance that incorporate correlations and non-Gaussianities, improving the robustness of cosmological data analysis.

Findings

Estimators show excellent agreement across methods.

No significant inconsistencies found in supernovae data.

Results support the robustness of local Hubble constant measurements.

Abstract

We develop estimators of agreement and disagreement between correlated cosmological data sets. These account for data correlations when computing the significance of both tensions and excess confirmation while remaining statistically optimal. We discuss and thoroughly characterize different approaches commenting on the ones that have the best behavior in practical applications. We complement the calculation of their statistical distribution within the Gaussian model with one estimator that takes non-Gaussianities fully into account. To illustrate the use of our techniques, we apply these estimators to supernovae measurements of the distance-redshift relation, absolutely calibrated by the local distance ladder. The suite of best estimators that we discuss finds results that are in excellent agreement between estimators and find no indications of significant internal inconsistencies in this data set above the $1\%$ probability threshold. This shows the robustness of local determinations of the Hubble constant to features in the distance-redshift relation.