Assessing tension metrics with Dark Energy Survey and Planck data

Abstract: Quantifying tensions -- inconsistencies amongst measurements of cosmological parameters by different experiments -- has emerged as a crucial part of modern cosmological data analysis. Statistically-significant tensions between two experiments or cosmological probes may indicate new physics extending beyond the standard cosmological model and need to be promptly identified. We apply several tension estimators proposed in the literature to the Dark Energy Survey (DES) large-scale structure measurement and Planck cosmic microwave background data. We first evaluate the responsiveness of these metrics to an input tension artificially introduced between the two, using synthetic DES data. We then apply the metrics to the comparison of Planck and actual DES Year 1 data. We find that the parameter differences, Eigentension, and Suspiciousness metrics all yield similar results on both simulated and real data, while the Bayes ratio is inconsistent with the rest due to its dependence on the prior volume. Using these metrics, we calculate the tension between DES Year 1 $3\times 2$pt and Planck, finding the surveys to be in $\sim 2.3\sigma$ tension under the $\Lambda$CDM paradigm. This suite of metrics provides a toolset for robustly testing tensions in the DES Year 3 data and beyond.