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Register a new userQuantifying Concordance in Cosmology
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Sebastian Seehars
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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.
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We propose a new intuitive metric for evaluating the tension between two experiments, and apply it to several data sets. While our metric is non-optimal, if evidence of tension is detected, this evidence is robust and easy to interpret. Assuming a flat $Lambda$CDM cosmological model, we find that there is a modest $2.2sigma$ tension between the DES Year 1 results and the ${it Planck}$ measurements of the Cosmic Microwave Background (CMB). This tension is driven by the difference between the amount of structure observed in the late-time Universe and that predicted from fitting the ${it Planck}$ data, and appears to be unrelated to the tension between ${it Planck}$ and local esitmates of the Hubble rate. In particular, combining DES, Baryon Acoustic Oscillations (BAO), Big-Bang Nucleosynthesis (BBN), and supernovae (SNe) measurements recovers a Hubble constant and sound horizon consistent with ${it Planck}$, and in tension with local distance-ladder measurements. If the tension between these various data sets persists, it is likely that reconciling ${it all}$ current data will require breaking the flat $Lambda$CDM model in at least two different ways: one involving new physics in the early Universe, and one involving new late-time Universe physics.
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