Overview of Tension Metrics in Cosmology

The 𝝠CDM model has been the standard cosmological model for many decades. However, with the ever-increasing precision of modern cosmological surveys that have provided percent-level constraints on cosmological parameters, we are starting to see many inconsistencies with this standard picture. The most well-known are the H₀ and the S₈ tensions. In this context, several tension metrics have been proposed with the aim of accurately quantifying the degree of discordances between datasets. We discuss some key tension metrics, their scope, and their features. We have reproduced some of the known tensions using datasets from DESI, DES-SNY5, Planck, among others. Apart from the possibility of unknown systematics, these tensions may be an indication of new physics beyond the standard model.