Consistency tests in cosmology using relative entropy

TL;DR

This paper explores the use of relative entropy (KL divergence) as a tool for assessing the consistency of cosmological data sets and models, introducing a new framework validated on supernova and CMB data.

Contribution

It revisits the properties of relative entropy as a consistency measure and introduces a novel model rejection framework based on posterior predictive distributions.

Findings

Validated the new method on toy models

Applied to supernova and CMB data for six cosmological models

Provided insights into data-model consistency in cosmology

Abstract

With the high-precision data from current and upcoming experiments, it becomes increasingly important to perform consistency tests of the standard cosmological model. In this work, we focus on consistency measures between different data sets and methods that allow us to assess the goodness of fit of different models. We address both of these questions using the relative entropy or Kullback-Leibler (KL) divergence [Kullback et al., 1951]. First, we revisit the relative entropy as a consistency measure between data sets and further investigate some of its key properties, such as asymmetry and path dependence. We then introduce a novel model rejection framework, which is based on the relative entropy and the posterior predictive distribution. We validate the method on several toy models and apply it to Type Ia supernovae data from the JLA and CMB constraints from Planck 2015, testing the consistency of the data with six different cosmological models.