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, $Q_{\rm DM}$, 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 $1.9σ$ (DR1) to $2.3σ$(DR2) is reinterpreted as a more modest shift from $1.18σ^{\rm eff}$ (DR1) to $1.45σ^{\rm eff}$ (DR2). These new tools may also prove valuable across research fields where dataset discrepancies arise.

Figures (5)

• Figure 1: Posterior distributions for three synthetic datasets in two contrasting configurations (upper panels), and the corresponding tension vectors in parameter-difference space (lower panels). The eigenvalues of $\mathcal{C}_{ab}$ quantify both the strength and geometric structure of the multi-dataset tension. Eigenvectors are also shown for reference ($\vec{v}_i$).
• Figure 2: Different configurations of three posterior distributions mapped to the equivalent reference setup consisting of three posteriors with identical covariances, and means positioned at the vertices of an equilateral triangle.
• Figure 3: PTE and corresponding $N_\sigma$ as a function of the side length $L$ of the reference equilateral-triangle configuration. Dotted lines indicate values of L equivalent to $N_\sigma^{\rm eff}=\{1,2,3\}$ in the shared parameter space.
• Figure 4: Example of posterior distributions under their gaussian approximation from real analyses using cosmological datasets.
• Figure 5: Sets of tension vectors for current cosmological datasets together with the corresponding eigenvalues and eccentricity.