Cosmological discordances. II. Hubble constant, Planck and large-scale-structure data sets

We examine systematically the (in) consistency between cosmological constraints as obtained from various current data sets of the expansion history, large-scale-structure (LSS), and cosmic microwave background (CMB) temperature and polarization from Planck. We run (dis) concordance tests within each set and across the three sets using a recently introduced index of inconsistency (IOI) capable of dissecting inconsistencies between two or more data sets. First, we compare the constraints on H₀ from five different methods and find that the IOI drops from 2. 85 to 0. 88 (on Jeffreys's scales) when the local H₀ measurements are removed. This seems to indicate that the local measurement is an outlier compared to the others, thus favoring a systematics-based explanation. We find a moderate inconsistency (IOI=2. 61) between Planck temperature and polarization data sets. We find that current LSS data sets including the WiggleZ power spectrum, SDSS redshift space distortion, CFHTLenS weak lensing, CMB lensing, and cluster count from SZ effect, are consistent one with another and also when all combined. However, we find a persistent moderate inconsistency between Planck and individual or combined LSS probes. For Planck TT+lowTEB versus individual LSS probes, the IOI spans the range 2. 92--3. 72 and increases to 3. 44--4. 20 when the polarization data is added in. The joint LSS versus the combined Planck temperature and polarization has an IOI of 2. 83 in the most conservative case. But if Planck low- temperature and polarization is also added to the joint LSS to constrain and break degeneracies, the inconsistency between Planck and joint LSS data increases to the high end of the moderate range with IOI=4. 81. Whether due to systematic effects in the data or to the underlying model, these inconsistencies need to be resolved. Finally, we perform forecast calculations using the Large Sky Synoptic Survey (LSST) and find that the discordance between Planck and future LSS data, if it persists as present, can rise up to a high IOI of 17, thus falling in the strong range of inconsistency.