Generalized tension metrics for multiple cosmological datasets

Abstract

We introduce a novel estimator to quantify statistical tensions among multiple cosmological datasets simultaneously. This estimator generalizes the Difference-in-Means statistic, $Q_{\mathrm{DM}}$, 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 $1.9\ddot{I}ƒ$ (DR1) to $2.3\ddot{I}ƒ$(DR2) is reinterpreted as a more modest shift from $1.18\ddot{I}{ƒ}^{\mathrm{eff}}$ (DR1) to $1.45\ddot{I}{ƒ}^{\mathrm{eff}}$ (DR2). These new tools may also prove valuable across research fields where dataset discrepancies arise.

6 pages, 5 figures, 2 tables