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

TL;DR

The paper employs the index of inconsistency (IOI) to quantify (in)consistencies among Planck CMB data, large-scale-structure probes, and local $H_0$ measurements. By comparing two- and multi-dataset IOIs, it identifies Planck–local $H_0$ as a likely outlier-driven tension ($IOI=5.83$) and uncovers persistent Planck–LSS discordances, especially when combining temperature and polarization data ($IOI$ up to about $4.81$). The LSS data themselves are mutually consistent, enabling robust joint analyses, though the Planck data, particularly in TT, drive the strongest cross-dataset tensions. Forecasts using LSST cosmic shear suggest that if current LSS best fits persist, Planck–LSST discordance could become extremely strong ($IOI=17$), highlighting the importance of forthcoming data in resolving the underlying cause—systematics or new physics.

Abstract

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) from Planck. We run (dis)concordance tests within each set and across the 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 $H_0$ from five different methods and find that the IOI drops from 2.85 to 0.88 (on Jeffreys' scales) when the local $H_0$ measurements is removed. This seems to indicate that the local measurement is an outlier, thus favoring a systematics-based explanation. We find a moderate inconsistency (IOI=2.61) between Planck temperature and polarization. We find that current LSS data sets including WiggleZ, SDSS RSD, CFHTLenS, CMB lensing and SZ cluster count, are consistent one with another and 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 lowTEB is added to the joint LSS to constrain $τ$ 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 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. (Abridged).

Figures (2)

• Figure 1: Examples of multiexperiment IOI. As shown above on the left panel, each of the three data sets is consistent with any other one, which is also shown by the three small two-experiment IOIs. But the three data sets are actually inconsistent as a whole because there is little common region simultaneously favored by the three data sets. On the other hand, the three data sets on the right panel are consistent one with another and also consistent when considered as a whole. The three-experiment IOI is able to distinguish between the two situations; IOI=5.3 on the left while IOI=0.21 on the right.
• Figure 2: A flowchart illustrating the algorithmic method we follow using the IOI measures to help identify the cause of inconsistency, if any. Explanations are provided in the text.