Physically-motivated priors in the local distance ladder significantly reduce the Hubble tension

TL;DR

This work demonstrates that the choice of priors in the local Cepheid–SN Ia distance ladder can significantly influence the inferred Hubble constant. By implementing physically motivated, volume-weighted priors on all distances and by jointly fitting Milky Way Cepheids with extragalactic data while conservatively handling the Gaia parallax offset, the authors obtain $H_0 = 70.6 \pm 1.0$ km s$^{-1}$ Mpc$^{-1}$, down from $H_0 = 73.0 \pm 1.0$ km s$^{-1}$ Mpc$^{-1}$ and reducing the tension with Planck from $5\sigma$ to $\sim2\sigma$. The analysis reveals coherent, ~3% upward shifts in distance moduli that propagate linearly into $H_0$ via Hubble’s law, underscoring the central role priors play in distance calibration. The results suggest that prior choices, often treated as innocuous defaults, can reconcile part of the Hubble tension and motivate re-evaluation of priors across all distance-ladder approaches.

Abstract

Determinations of the Hubble constant based on the local distance ladder remain in significant tension with early-Universe inferences from the cosmic microwave background. While this tension is often discussed in terms of new physics or unmodeled systematics, the role of the assumed priors on the model parameters has received comparatively little attention. Recently, Desmond et al. (2025) pointed out that the commonly adopted flat prior on distance moduli upweights smaller distances and systematically favors high inferred values of the Hubble constant. Motivated by this observation, we perform a comprehensive Bayesian recalibration of the distance ladder, applying physically motivated priors uniformly to all distances, including the Milky Way Cepheids, which are incorporated directly into the joint fit. Together with a conservative treatment of the Gaia EDR3 residual parallax offset, the Hubble constant shifts from $H_0 = 73.0 \pm 1.0 \, \mathrm{km/s/Mpc}$ to $H_0 = 70.6 \pm 1.0 \, \mathrm{km/s/Mpc}$, reducing the Hubble tension from $5 \, σ$ to $2 \, σ$. Our results show that the assumed priors -- often treated as innocuous defaults -- may play a central role in the Hubble tension. Because all local distance ladders rely on the calibration of distances, similar prior-driven effects are expected to arise across distance-ladder methods.

Figures (4)

• Figure 1: Normalized posterior distributions of the Hubble constant inferred under different prior assumptions. SH0ES-ref corresponds to the reference calibration, yielding $H_0 = 72.7 \pm 1.0 \, \mathrm{km/s/Mpc}$. Phys-prior shows the result obtained with the physically motivated distance priors and a flat prior on the residual Gaia parallax offset, giving $H_0 = 70.6 \pm 1.0 \, \mathrm{km/s/Mpc}$. The Planck curve indicates the CMB-based constraint, $H_0 = 67.4 \pm 0.5 \, \mathrm{km/s/Mpc}$. Under physically motivated priors, the tension with Planck is reduced to $2\,\sigma$.
• Figure 2: Marginalized posterior distributions in the $(M_H^W, zp)$ plane for the Phys-prior (blue) and SH0ES-ref (dashed) calibrations. In SH0ES-ref, a Gaussian prior is imposed on $zp$, whereas in the Phys-prior case a flat prior is adopted. Allowing the data to constrain $zp$ directly shifts the posterior toward more negative values of $zp$ and brighter $M_H^W$, contributing to the lower inferred value of $H_0$.
• Figure 3: Shifts in inferred distance moduli relative to the reference calibration, $\mu_{\rm Phys\text{-}prior} - \mu_{\rm SH0ES\text{-}ref}$. Top: distance-ladder galaxies. Bottom: MW Cepheids. Error bars show posterior uncertainties from SH0ES-ref. The physically motivated distance prior produces coherent positive shifts, larger for more weakly constrained distances. The mean shifts are $0.066\,\mathrm{mag}$ for SN Ia hosts and $0.057\,\mathrm{mag}$ for MW Cepheids, corresponding to average distance increases of $3.0\%$ and $2.6\%$, respectively, which drive the associated change in $H_0$.
• Figure 4: Constraints on the Hubble constant inferred from the local distance ladder when anchored to individual geometric calibrators. Shown are marginalized $H_0$ constraints obtained using the MW, the LMC, and NGC 4258 as anchors for the SH0ES-ref calibration (blue) and the calibration with physically motivated priors (red). The horizontal gray band indicates the Planck CMB constraint. Physically motivated distance priors shift $H_0$ downward for all anchors while preserving their mutual consistency, thereby reducing the tension with the CMB.