1.8 per cent measurement of $H_0$ from Cepheids alone

One of the most pressing problems in current cosmology is the cause of the Hubble tension. We revisit a two-rung distance ladder, composed only of Cepheid periods and magnitudes, anchor distances in the Milky Way, Large Magellanic Cloud, NGC 4258, and host galaxy redshifts. We adopt the SH0ES data for the most up-to-date and carefully vetted measurements, where the Cepheid hosts were selected to harbour also Type Ia supernovae. We introduce two important improvements: a rigorous selection modelling and a state-of-the-art density and peculiar velocity model using Manticore-Local, based on the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm. We infer $H_0 = 71.7 \pm 1.3,\mathrm{km},\mathrm{s}^{-1},\mathrm{Mpc}^{-1}$, assuming the Cepheid host sample was selected by supernova magnitudes. However, the actual selection criteria are not clear, and other assumptions can increase $H_0$ by up to one statistical standard deviation. The posterior has a lower central value and a 45 per cent smaller uncertainty than a previous study using the same distance-ladder data. The result is also slightly lower than the supernova-based SH0ES inferred value of $H_0 = 73.2 \pm 0.9,\mathrm{km},\mathrm{s}^{-1},\mathrm{Mpc}^{-1}$, and is in $3.3σ$ tension with the latest cosmic microwave background results in the standard cosmological model. These results demonstrate that a measurement of $H_0$ of sufficient precision to weigh in on the Hubble tension is achievable using second-rung data alone, underscoring the importance of robust and accurate statistical and velocity-field modelling.

💡 Research Summary

This paper revisits the local distance ladder by stripping it down to its second rung – Cepheid variable stars – and asks whether a precise measurement of the Hubble constant (H₀) can be obtained without invoking Type Ia supernovae (SNe). Using the latest SH0ES catalogue, the authors adopt the same three geometric anchors as the full SH0ES analysis: Milky Way Cepheids with Gaia and HST spatial‑scan parallaxes, detached eclipsing binaries in the Large Magellanic Cloud, and the water‑maser distance to NGC 4258. These anchors fix the absolute magnitude (M_W), period‑luminosity slope (b_W) and metallicity term (Z_W) of the Cepheid period‑luminosity relation (CPLR).

The sample consists of 35 galaxies that host both Cepheids and SNe, all within ≈ 40 Mpc (cz < 3300 km s⁻¹). Their redshifts are taken from the Pantheon+ compilation and transformed to the CMB frame. Crucially, the authors argue that this subset was selected not by random chance but by a hard cut on the apparent magnitude of the associated SNe (m_SN < 14 mag) together with the redshift limit. Kolmogorov–Smirnov tests show that the magnitude and redshift distributions of the 35 hosts are statistically consistent with the full Pantheon+ sample after applying the same cuts, supporting the hypothesis of a joint magnitude‑and‑redshift selection.

Methodologically the paper introduces two major improvements over previous Cepheid‑only analyses (most notably Kenworthy et al. 2022, hereafter K22). First, the selection function is modelled explicitly within a Bayesian forward‑modelling framework. The probability that a galaxy enters the Cepheid host sample is expressed as a joint function of SN apparent magnitude and host redshift, and this function is propagated through the likelihood. By varying the assumed form of the selection (e.g., magnitude‑only, redshift‑only, or the joint cut) the authors demonstrate that H₀ can shift by up to ≈ 1 σ, highlighting the importance of accounting for selection bias.

Second, the treatment of peculiar velocities (PVs) is upgraded. While K22 employed the linear reconstruction of Carrick et al. (2015), this work uses the state‑of‑the‑art Manticore‑Local reconstruction, which is based on the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm. Manticore‑Local provides a three‑dimensional density and velocity field inferred from the observed galaxy distribution, allowing the authors to compute a full PV covariance matrix for the 35 hosts. Tests on mock catalogues show that this model reduces PV‑induced uncertainties by roughly 30 % compared with the Carrick approach, and that any residual bias in H₀ is below 0.1 km s⁻¹ Mpc⁻¹.

The Cepheid likelihood incorporates the full covariance of the observed magnitudes (Σ_Ceph), which includes contributions from metallicity systematics, background‑induced photometric biases (estimated via artificial‑star injections), and intrinsic scatter. The Milky Way parallax constraints are introduced as priors on M_W from two independent samples (HST spatial scans and Gaia EDR3).

Running the full Bayesian inference, the authors obtain

H₀ = 71.7 ± 1.3 km s⁻¹ Mpc⁻¹

This value is 1.5 km s⁻¹ Mpc⁻¹ lower than the SH0ES result that combines Cepheids and SNe (73.2 ± 0.9) and remains in 3.3 σ tension with the Planck CMB inference (≈ 67.4 km s⁻¹ Mpc⁻¹ in ΛCDM). The quoted uncertainty is 45 % smaller than that reported by K22 (H₀ = 72.9 +2.4/−2.2), reflecting the combined impact of the more rigorous selection modelling and the improved PV reconstruction.

The paper includes extensive validation: mock catalogues with known H₀ are processed through the full pipeline to confirm unbiased recovery; alternative selection functions are explored to quantify systematic shifts; and a comparison with the Carrick PV model is presented, showing consistent central values but larger error bars.

In the discussion, the authors emphasize that a Cepheid‑only ladder can achieve ≈ 1.8 % precision, sufficient to weigh in on the Hubble tension. They argue that further reductions in uncertainty are feasible with larger Cepheid samples (e.g., from JWST or future HST programs) and with even higher‑resolution PV reconstructions. The work also serves as a benchmark for testing the robustness of the full SH0ES analysis: if the Cepheid‑only result, which avoids the complex SN standardisation pipeline, still yields a high H₀, the tension is less likely to be driven by SN‑related systematics. Conversely, the modestly lower central value hints that the SN step may contribute a small upward bias, though not enough to resolve the tension entirely.

Overall, the study demonstrates that careful statistical treatment of selection effects and state‑of‑the‑art peculiar‑velocity modelling can extract a high‑precision H₀ from second‑rung data alone, providing an independent check on the classic Cepheid‑SN distance ladder and sharpening the debate over whether new physics or hidden systematics underlie the Hubble tension.