Clarifying the Hubble constant tension with a Bayesian hierarchical model of the local distance ladder

• Published in: Monthly notices of the Royal Astronomical Society Vol. 476; no. 3; pp. 3861 - 3882
• Main Authors: Feeney, Stephen M, Mortlock, Daniel J, Dalmasso, Niccolò
• Format: Journal Article
• Language: English
• Published: Oxford University Press 21-05-2018
• Subjects: cosmic background radiation; distance scale; methods: statistical; cosmic background radiation; distance scale; methods: statistical
• ISSN: 0035-8711; 1365-2966; 1365-2966
• DOI: 10.1093/mnras/sty418

Abstract
Estimates of the Hubble constant, H0, from the local distance ladder and from the cosmic microwave background (CMB) are discrepant at the ∼3σ level, indicating a potential issue with the standard Λ cold dark matter (ΛCDM) cosmology. A probabilistic (i.e. Bayesian) interpretation of this tension requires a model comparison calculation, which in turn depends strongly on the tails of the H0 likelihoods. Evaluating the tails of the local H0 likelihood requires the use of non-Gaussian distributions to faithfully represent anchor likelihoods and outliers, and simultaneous fitting of the complete distance-ladder data set to ensure correct uncertainty propagation. We have hence developed a Bayesian hierarchical model of the full distance ladder that does not rely on Gaussian distributions and allows outliers to be modelled without arbitrary data cuts. Marginalizing over the full ∼3000-parameter joint posterior distribution, we find H0 = (72.72 ± 1.67) km s−1 Mpc−1 when applied to the outlier-cleaned Riess et al. data, and (73.15 ± 1.78) km s−1 Mpc−1 with supernova outliers reintroduced (the pre-cut Cepheid data set is not available). Using our precise evaluation of the tails of the H0 likelihood, we apply Bayesian model comparison to assess the evidence for deviation from ΛCDM given the distance-ladder and CMB data. The odds against ΛCDM are at worst ∼10:1 when considering the Planck 2015 XIII data, regardless of outlier treatment, considerably less dramatic than naïvely implied by the 2.8σ discrepancy. These odds become ∼60:1 when an approximation to the more-discrepant Planck Intermediate XLVI likelihood is included.