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

Stephen M. Feeney; Daniel J. Mortlock; Niccolò Dalmasso

doi:10.1093/mnras/sty418

paper

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

arXiv:1707.00007 · doi:10.1093/mnras/sty418

Abstract

Estimates of the Hubble constant, $H_{0}$ , from the distance ladder and the cosmic microwave background (CMB) differ at the $\sim$ 3- $σ$ level, indicating a potential issue with the standard $Λ$ CDM cosmology. Interpreting this tension correctly requires a model comparison calculation depending on not only the traditional ` $n$ - $σ$ ' mismatch but also the tails of the likelihoods. Determining the form of the tails of the local $H_{0}$ likelihood is impossible with the standard Gaussian least-squares approximation, as it requires using non-Gaussian distributions to faithfully represent anchor likelihoods and model outliers in the Cepheid and supernova (SN) populations, and simultaneous fitting of the full distance-ladder dataset to correctly propagate uncertainties. We have developed a Bayesian hierarchical model that describes the full distance ladder, from nearby geometric anchors through Cepheids to Hubble-Flow SNe. This model does not rely on any distributions being Gaussian, allowing outliers to be modeled and obviating the need for arbitrary data cuts. Sampling from the $\sim$ 3000-parameter joint posterior using Hamiltonian Monte Carlo, we find $H_{0}$ = (72.72 $\pm$ 1.67) $km s^{- 1} Mp c^{- 1}$ when applied to the outlier-cleaned Riess et al. (2016) data, and ( $73.15 \pm 1.78$ ) $km s^{- 1} Mp c^{- 1}$ with SN outliers reintroduced. Our high-fidelity sampling of the low- $H_{0}$ tail of the distance-ladder likelihood allows us to apply Bayesian model comparison to assess the evidence for deviation from $Λ$ CDM. We set up this comparison to yield a lower limit on the odds of the underlying model being $Λ$ CDM given the distance-ladder and Planck XIII (2016) CMB data. The odds against $Λ$ CDM are at worst 10:1 or 7:1, depending on whether the SNe outliers are cut or modeled, or 60:1 if an approximation to the Planck Int. XLVI (2016) likelihood is used.

24 pages, 14 figures, matches version submitted to MNRAS. The model code used in this analysis is available for download at https://github.com/sfeeney/hh0

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

Abstract

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