Quantifying Concordance in Cosmology

TL;DR

This paper revisits the Surprise measure based on relative entropy to quantify agreement between cosmological datasets, demonstrating its effectiveness in identifying tensions and shifts among WMAP and Planck constraints on the DM model.

Contribution

It refines the properties of the Surprise measure and compares it with other concordance metrics, applying it to analyze WMAP and Planck data for the first time.

Findings

Large Surprise indicates tension between WMAP 9 and Planck 13 due to amplitude shifts.

Planck 15 constraints are consistent with WMAP 9, reducing previous tensions.

Surprise effectively quantifies dataset agreement and shifts in cosmological parameters.

Abstract

Quantifying the concordance between different cosmological experiments is important for testing the validity of theoretical models and systematics in the observations. In earlier work, we thus proposed the Surprise, a concordance measure derived from the relative entropy between posterior distributions. We revisit the properties of the Surprise and describe how it provides a general, versatile, and robust measure for the agreement between datasets. We also compare it to other measures of concordance that have been proposed for cosmology. As an application, we extend our earlier analysis and use the Surprise to quantify the agreement between WMAP 9, Planck 13 and Planck 15 constraints on the $\Lambda$CDM model. Using a principle component analysis in parameter space, we find that the large Surprise between WMAP 9 and Planck 13 (S = 17.6 bits, implying a deviation from consistency at 99.8% confidence) is due to a shift along a direction that is dominated by the amplitude of the power spectrum. The Planck 15 constraints deviate from the Planck 13 results (S = 56.3 bits), primarily due to a shift in the same direction. The Surprise between WMAP and Planck consequently disappears when moving to Planck 15 (S = -5.1 bits). This means that, unlike Planck 13, Planck 15 is not in tension with WMAP 9. These results illustrate the advantages of the relative entropy and the Surprise for quantifying the disagreement between cosmological experiments and more generally as an information metric for cosmology.