Cosmological discordances. III. More on measure properties, large-scale-structure constraints, the Hubble constant and Planck data

Consistency between cosmological datasets is essential for ongoing and future cosmological analyses. We first investigate the questions of stability and applicability of some moment-based inconsistency measures to multiple datasets. We show that the recently introduced index of inconsistency (IOI) is numerically stable while it can be applied to multiple datasets. We use an illustrative construction of constraints as well as an example with real datasets (i.e., WMAP versus Planck) to show some limitations of the application of the Karhunen-Loeve decomposition to discordance measures. Second, we perform various consistency analyses using IOI between multiple current datasets while working with the entire common parameter spaces. We find current large-scale-structure (LSS) datasets [Planck cosmic microwave background lensing, Dark Energy Survey (DES) lensing clustering, and sloan digital sky survey, redshift space distorsions] all to be consistent with one another. This is found to not be the case for Planck temperature (temperature auto correlation, TT) versus polarization [temperature and E-mode polarization cross correlation (TE), E-mode polarization auto correlation (EE)] data, where moderate inconsistencies are present. Noteworthy, we find a strong inconsistency between joint LSS probes and Planck with IOI =5.27 , and a moderate tension between DES and Planck with IOI =3.14 . Next, using the IOI metric, we compare the Hubble constant from five independent probes. We confirm previous strong tensions between local measurement (Supernovae, HO, for the equation of state of dark energy, SH0ES) and Planck as well as between H0 lenses in COSMOGRAIL's wellspring and Planck, but also find new strong tensions between SH0ES measurement and the joint LSS probes with IOI =6.73 (i.e., 3.7 -σ in one dimension) as well as between joint LSS and combined probes SH 0 ES +H 0 LiCOW with IOI =8.59 (i.e., 4.1 -σ in one dimension). Whether because of systematic effects in the datasets or problems with the underlying model, sources of these old and new tensions need to be identified and dealt with.