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

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.

💡 Research Summary

The paper addresses a largely overlooked source of bias in local distance‑ladder measurements of the Hubble constant: the choice of priors on distance‑related parameters. While the tension between the locally measured H₀ (≈73 km s⁻¹ Mpc⁻¹) and the early‑Universe value inferred from Planck CMB data (≈67.4 km s⁻¹ Mpc⁻¹) has motivated extensive searches for new physics or hidden systematics, the statistical assumptions underlying the ladder have received comparatively little scrutiny.

Desmond et al. (2025) recently pointed out that the standard SH0ES analysis adopts a flat prior on distance moduli (π(µ)=const), which translates into an inverse distance prior π(D)∝D⁻¹. This prior unintentionally up‑weights nearer objects, biasing the inferred H₀ upward. Physically, a homogeneous, volume‑limited sample of distance indicators should follow a prior proportional to the accessible volume, i.e., π(D)∝D². In logarithmic form this becomes ln π(µ)=0.6 ln 10 µ.

The authors perform a full Bayesian recalibration of the fourth‑iteration SH0ES distance ladder, incorporating all Cepheids—including those in the Milky Way—into a single joint likelihood. This unified framework allows them to impose the physically motivated distance prior uniformly on every distance modulus, and to replace the Gaussian prior on the residual Gaia EDR3 parallax zero‑point offset (zp) with a flat prior, thereby letting the data constrain zp directly.

The model contains 113 parameters: distance moduli for 37 SN‑Ia host galaxies, three anchor distances (MW, LMC, NGC 4258), Cepheid period‑luminosity‑metallicity parameters, the SN‑Ia absolute magnitude, the Hubble constant (parameterized as 5 log₁₀ H₀), 66 individual MW Cepheid distance moduli, and the residual parallax offset. The likelihood combines a linear Gaussian component for all photometric observables with a non‑linear term for the MW Cepheid parallaxes. Sampling is performed with the affine‑invariant MCMC ensemble sampler (emcee), ensuring convergence through standard autocorrelation diagnostics.

A reference calibration (“SH0ES‑ref”) reproduces the standard SH0ES result (H₀≈72.7 ± 1.0 km s⁻¹ Mpc⁻¹) by using flat priors on all parameters except for weak Gaussian priors on zp (σ=0.01 mas) and the ground‑to‑HST photometric zero‑point. When the physically motivated distance prior and a flat zp prior are adopted (the “Phys‑prior” model), the inferred H₀ drops to 70.6 ± 1.0 km s⁻¹ Mpc⁻¹—a shift of 2.1 km s⁻¹ Mpc⁻¹. Roughly 1.7 km s⁻¹ Mpc⁻¹ of this change is driven directly by the distance prior, while the remaining 0.4 km s⁻¹ Mpc⁻¹ stems from allowing zp to be determined by the ladder itself.

The distance moduli of the SN‑Ia host galaxies increase on average by 0.066 mag (≈3 % in distance), and the MW Cepheids shift by 0.057 mag (≈2.6 %). Because Hubble’s law relates recession velocity to distance (cz = H₀ D), a 3 % increase in distance translates into a comparable 3 % decrease in H₀, fully accounting for the observed shift. The effect is strongest for objects with larger statistical uncertainties, reflecting the prior’s greater influence where the data are less informative.

The authors also explore calibrations anchored to each geometric distance indicator separately (MW, LMC, NGC 4258). In every case, the physically motivated prior pushes H₀ to lower values, confirming that the prior effect is not tied to a specific anchor but is intrinsic to the ladder’s statistical structure.

The key implication is that the prior choice—often treated as a harmless default—can induce a systematic bias of order a few km s⁻¹ Mpc⁻¹ in H₀, enough to halve the reported tension with Planck. This suggests that similar prior‑driven effects may be present in other distance‑ladder methods (e.g., tip‑of‑the‑red‑giant‑branch, surface‑brightness fluctuations). Consequently, resolving the Hubble tension may require not only new physics or improved systematics control but also a careful, physically justified formulation of statistical priors, especially for Gaia parallaxes and other fundamental calibrators.

In summary, by replacing the flat distance‑modulus prior with a volume‑weighted D² prior and adopting a conservative flat prior on the Gaia parallax offset, the authors demonstrate that the local distance ladder yields H₀ = 70.6 ± 1.0 km s⁻¹ Mpc⁻¹, reducing the discrepancy with the CMB inference from 5σ to 2σ. This work highlights the central role of prior assumptions in cosmological inference and calls for a reassessment of statistical practices across all distance‑ladder techniques.