# Planck confronts large scale structure: methods to quantify discordance

## TL;DR

This paper evaluates the level of discordance between Planck CMB data and large scale structure probes using various statistical measures, updating previous analyses with new data and methods to assess tensions in cosmological parameters.

## Contribution

It introduces updated methods and data to quantify the tension between CMB and LSS data, showing reduced discordance compared to earlier studies.

## Key findings

- The tension between Planck and LSS data is minor, around 0.76σ to 2.55σ depending on the data combination.
- Updated analysis shows greater agreement between CMB and LSS constraints with new data.
- The paper discusses and compares different statistical measures for quantifying discordance.

## Abstract

Discordance in the $\Lambda$CDM cosmological model can be seen by comparing parameters constrained by CMB measurements to those inferred by probes of large scale structure. Recent improvements in observations, including final data releases from both Planck and SDSS-III BOSS, as well as improved astrophysical uncertainty analysis of CFHTLenS, allows for an update in the quantification of any tension between large and small scales. This paper is intended, primarily, as a discussion on the quantifications of discordance when comparing the parameter constraints of a model when given two different data sets. We consider KL-divergence, comparison of Bayesian evidences and other statistics which are sensitive to the mean, variance and shape of the distributions. However, as a by-product, we present an update to the similar analysis in (Battye, Charnock and Moss; 2015) where we find that, considering new data and treatment of priors, the constraints from the CMB and from a combination of LSS probes are in greater agreement and any tension only persists to a minor degree. In particular, we find the parameter constraints from the combination of LSS probes which are most discrepant with the Planck2015+Pol+BAO parameter distributions can be quantified at a 2.55$\sigma$ tension using the method introduced in (Battye, Charnock and Moss; 2015). If instead we use the distributions constrained by the combination of LSS probes which are in greatest agreement with those from Planck2015+Pol+BAO this tension is only 0.76$\sigma$.