Cosmological discordances: A new measure, marginalization effects, and application to geometry versus growth current data sets

The continuous progress toward more precise cosmological surveys and experiments has galvanized recent interest into consistency tests on cosmological parameters and models. At the heart of this effort is quantifying the degree of inconsistency between two or more cosmological data sets. We introduce an intuitive moment-based measure we call the index of inconsistency (IOI) and show that it is sensitive to the separation of the means, the size of the constraint ellipsoids, and their orientations in the parameter space. We find that it tracks accurately the inconsistencies when present. Next, we show that parameter marginalization can cause a loss of information on the inconsistency between two experiments, and we quantify such a loss using the drop in IOI. In order to zoom on a given parameter, we define the relative residual IOI and the relative drop in IOI. While these two quantities can provide insights on the parameters that are most responsible for inconsistencies, we find that the full IOI applied to the whole parameter spaces is what must be used to correctly reflect the degree of inconsistency between two experiments. We discuss various properties of IOI, provide its eigenmode decomposition, and compare it to other measures of discordance. Finally, we apply IOI to current geometry data sets (i.e., an improved Supernovae Type Ia compilation, baryon acoustic oscillations from 6dF, SDSS MGS and Lyman-alpha forest, and high-l cosmic microwave background (CMB) temperature data from Planck-2015) versus growth data sets (i.e., Redshift Space Distortions from WiggleZ and SDSS, Weak Lensing from CFHTLenS, CMB Lensing, Sunyav-Zeldovich effect, and low-l CMB temperature and polarization data from Planck-2015). We find that a persistent inconsistency is present between the two data sets. This could reflect the presence of systematics in the data or inconsistencies in the underlying model.