Concordance and discordance in cosmology

The success of present and future cosmological studies is tied to the ability to detect discrepancies in complex data sets within the framework of a cosmological model. Tensions caused by the presence of unknown systematic effects need to be isolated and corrected to increase the overall accuracy of parameter constraints, while discrepancies due to new physical phenomena need to be promptly identified. We develop a full set of estimators of internal and mutual agreement and disagreement, whose strengths complement each other. These estimators take into account the effect of prior information and compute the statistical significance of both tensions and confirmatory biases. The estimators that we present optimally weight all parameter space directions that are either fully constrained by the data or the prior, allowing for complete and fair degree of freedom counting. We apply them to a wide range of state-of-the-art cosmological probes and show that these estimators can be easily used, regardless of model and data complexity. We derive a series of results that show that discrepancies indeed arise within the standard model. Several of them exceed the probability threshold of 95% and deserve a dedicated effort to understand their origin.