Generalized tension metrics for multiple cosmological datasets

TL;DR

This paper presents a new statistical estimator to measure and interpret tensions among multiple cosmological datasets, offering a geometric perspective and refining previous tension assessments.

Contribution

It introduces a generalized tension estimator for multiple datasets, enabling detection of dominant tension directions and providing a geometric interpretation.

Findings

Reinterpreted the tension between DESI and Planck datasets with a more modest significance shift.

Provided a geometric framework for understanding dataset tensions in multi-dimensional parameter space.

Demonstrated the estimator's potential applicability across various research fields with dataset discrepancies.

Abstract

We introduce a novel estimator to quantify statistical tensions among multiple cosmological datasets simultaneously. This estimator generalizes the Difference-in-Means statistic, $Q_{\rm DM}$, to the multi-dataset regime. Our framework enables the detection of dominant tension directions in the shared parameter space. It further provides a geometric interpretation of the tension for the two- and three-dataset cases in two dimensions. According to this approach, the previously reported increase in tension between DESI and Planck from $1.9\sigma$ (DR1) to $2.3\sigma$(DR2) is reinterpreted as a more modest shift from $1.18\sigma^{\rm eff}$ (DR1) to $1.45\sigma^{\rm eff}$ (DR2). These new tools may also prove valuable across research fields where dataset discrepancies arise.