# Integrated cosmological probes: Concordance quantified

## TL;DR

This study assesses the consistency of various cosmological data sets within the flat mbda CDM model using the Surprise statistic, finding all data sets are compatible at less than 1cc level when assumptions are consistent.

## Contribution

It extends previous integrated analyses by quantifying the concordance of multiple cosmological probes using the Surprise statistic, highlighting the importance of consistent model assumptions.

## Key findings

- All data sets are consistent within 1cccc level under consistent assumptions.
- Inconsistent neutrino mass assumptions can break the invariance of the Surprise statistic.
- When assumptions are aligned, the data agree with mbda CDM without tensions.

## Abstract

Assessing the consistency of parameter constraints derived from different cosmological probes is an important way to test the validity of the underlying cosmological model. In an earlier work [Nicola et al., 2017], we computed constraints on cosmological parameters for $\Lambda$CDM from an integrated analysis of CMB temperature anisotropies and CMB lensing from Planck, galaxy clustering and weak lensing from SDSS, weak lensing from DES SV as well as Type Ia supernovae and Hubble parameter measurements. In this work, we extend this analysis and quantify the concordance between the derived constraints and those derived by the Planck Collaboration as well as WMAP9, SPT and ACT. As a measure for consistency, we use the Surprise statistic [Seehars et al., 2014], which is based on the relative entropy. In the framework of a flat $\Lambda$CDM cosmological model, we find all data sets to be consistent with one another at a level of less than 1$\sigma$. We highlight that the relative entropy is sensitive to inconsistencies in the models that are used in different parts of the analysis. In particular, inconsistent assumptions for the neutrino mass break its invariance on the parameter choice. When consistent model assumptions are used, the data sets considered in this work all agree with each other and $\Lambda$CDM, without evidence for tensions.