A 1.8% measurement of the Hubble constant from Cepheids alone

Background

A central problem in contemporary cosmology is the persistent discrepancy between measurements of the expansion rate of the Universe, the Hubble constant $H_0$, inferred from the early and late Universe. The Planck satellite, analysing the cosmic microwave background within the ΛCDM framework, yields $H_0 = 67.4 \pm 0.5$ km/s/Mpc. Local distance–ladder measurements by the SH0ES collaboration, tying Cepheids to Type Ia supernovae (SNe), give $H_0 = 73.0 \pm 1.0$ km/s/Mpc. This statistical disagreement is at the 5σ level, which — if the statistics are robust and no significant systematics are unaccounted for — is currently our best evidence for physics beyond ΛCDM.

Just how reliable is the SH0ES inference of H₀, and how can we cross-check it? SH0ES constructs a distance ladder in three steps:

  1. geometric anchors — Milky Way parallaxes, detached eclipsing binaries in the Large Magellanic Cloud, and megamasers in NGC 4258 — calibrate the Cepheid period—luminosity relation;
  2. Cepheids in SN host galaxies calibrate the luminosity of SNe; and
  3. the calibrated SNe trace out the Hubble diagram to z ≈ 0.15, the low-redshift slope of which gives H₀.

SNe are crucial objects here, but also the most disputed — their use in SH0ES requires light-curve standardisation, host-environment corrections, dust modelling and simulation-based selection corrections — and there are multiple claims in the literature that mismodelling of SNe could be partially or wholly responsible for a merely apparent Hubble tension.

The most direct and powerful way to stress-test the ladder is therefore to remove the SNe entirely and use only geometric anchors and Cepheid hosts — a two-rung ladder in the spirit of Hubble’s original approach. The problem is that this removes the objects in the “Hubble flow” where velocities are dominated by expansion; for the objects retained (within ~40 Mpc), a precise and accurate peculiar velocity model is crucial to separate cosmological from structure-induced redshifts. Our work leverages state-of-the-art peculiar velocity fields from the BORG algorithm to deliver the first robust and high-precision constraint on H₀ without SNe or any other third-rung distance indicator.

A Bayesian hierarchical model with robust velocity fields

DAG image Directed acyclic graph of the hierarchical model, showing the connections between geometric anchors, the Cepheid period–luminosity relation, selection treatment, peculiar velocity modelling and $H_0$.

We construct a Bayesian hierarchical model for the Cepheid period–luminosity relation, latent host-galaxy distances, selection effects and the Hubble constant. Unlike approaches that first estimate distances and then use them in a separate Hubble diagram fit, our method treats all components simultaneously and self-consistently in a fully forward model. Cepheid apparent magnitudes, host-galaxy redshifts, and calibration anchors all inform a single posterior for the distances and cosmological parameters.

Besides the clarity of the statistical framework the key innovation is two-fold. First, we model peculiar velocities using Manticore-Local (hereafter Manticore), a state-of-the-art density and velocity reconstruction of the nearby Universe built on the BORG algorithm. Manticore supplies full posterior samples of the large-scale structure and corresponding velocity fields, resimulated with an N-body code for increased resolution. This approach quantifies reconstruction uncertainties and outperforms all other reconstructions in velocity field and cluster reconstruction. Second, we implement a robust forward model for selection effects. The set of SH0ES Cepheid hosts is not a random subset of galaxies, but neither does it derive from a well-defined procedure since dispirate observational samples from mutiple observing campaigns are compiled. We develop models based on apparent magnitude, redshift and joint selection, allowing us to quantify precisely their effect on the inferred Hubble constant and provide a robust systematic uncertainty associated with selection effects.

The Hubble constant without supernovae

Posterior distribution Posteriors on $H_0$ under differentselection models for the Manticore velocity field. The result clearly exceeds the Planck value in all cases.

With the fiducial model — uniform-in-volume priors on galaxy distances, SN-magnitude selection, and Manticore velocity fields — the inferred Hubble constant is: \(H_0 = 71.7 \pm 1.3 \mathrm{km s}^{-1}\mathrm{Mpc}^{-1}\)

This 1.8% constraint rivals the precision of three-rung distance-ladder estimates, including SH0ES itself, while completely omitting SNe as distance tracers. The central value is slightly lower than the SH0ES result, but consistent within ~1σ. The result differs from the Planck ΛCDM inference at 3.3σ, independently confirming that $H_0$ values unexpectedly high in ΛCDM are not driven exclusively by SNe. Further, model variations illustrate the sensitivity to uncertain assumptions: neglecting selection effects and simplifying the velocity treatment shifts $H_0$ downward by at most ~3 km/s/Mpc, while replacing Manticore with earlier reconstructions reduces precision by up to 60% — neither of which is sufficient to achieve consistency with the Planck value.

Looking forward, our work has three main implications. First, the case for a Hubble tension — and hence physics beyond ΛCDM — is strengthened because we now know that it cannot be driven purely by SNe. Second, the high precision we achieve bodes well for sub-1% inferences of H₀ from two-rung distance ladders to be achievable in the future. We used only a small subset of available primary and secondary distance indicators — a more comprehensive collection would beat down statistical uncertainties dramatically. This is afforded principally by the improved velocity modelling of BORG, which largely overcomes the need to probe the Hubble flow where peculiar velocities are unimportant but unknown systematics may also enter. Finally, our work highlights the crucial role played by selection effects, which provide an irreducible systematics floor if they cannot be modelled reliably. This implies that future observational samples should prioritise the application of clean, homogeneous selection criteria.

In summary, future improvements in BORG-based models coupled with next-generation survey data should provide the definitive word on the local value of $H_0$, and hence the validity of ΛCDM.

H0 measurement comparison Comparison of our results with others in the literature. We achieve a constraint almost as precise as SH0ES without any third rung whatsoever. Carrick+2015 is an older peculiar velocity reconstruction.

References