A new measure of tension between experiments

Tensions between cosmological measurements by different surveys or probes have always been important --- and are presently much discussed --- as they may lead to evidence of new physics. Several tests have been devised to probe the consistency of datasets given a cosmological model, but they often have undesired features such as dependence on the prior volume, or burdensome requirements such as that of near-Gaussian posterior distributions. We propose a new quantity, defined in a similar way as the Bayesian evidence ratio, in which these undesired properties are absent. We test the quantity on simple models with Gaussian and non-Gaussian likelihoods. We then apply it to data from the Planck satellite: we investigate the consistency of $\Lambda$CDM model parameters obtained from TT and EE angular power spectrum measurements, as well as the mutual consistency of cosmological parameters obtained from large scale (multipoles, $\ell<1000$) and small scale ($\ell \geq 1000$) portions of each measurement and find no significant discrepancy in the six-dimensional $\Lambda$CDM parameter space.