1.8 per cent measurement of $H_0$ from Cepheids alone

Abstract

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.

Figures (13)

• Figure 1: Distribution of SN apparent magnitudes for the 35 Cepheid host galaxies and their observed host redshifts either below a limiting SN magnitude of 14 mag or host observed redshift of $3300\,\mathrm{km}\,\mathrm{s}^{-1}$ (left and right panels, respectively). Following a Kolmogorov-Smirnov test, the two samples are mutually consistent with $p = 0.94$ and $p=0.60$. Assuming that the Pantheon+ sample is complete within ${\sim} 40\,\mathrm{Mpc}$, this implies random selection of Cepheid hosts below a limiting SN apparent magnitude of 14 and a host observed redshift of $3300\,\mathrm{km}\,\mathrm{s}^{-1}$. The error bars are $1\sigma$ Poisson counting errors. In addition, the dotted black lines show the magnitude distribution of Pantheon+ hosts with observed redshifts below $3300~\,\mathrm{km}\,\mathrm{s}^{-1}$ in the left panel, and the redshift distribution of hosts with magnitudes below 14 in the right panel. Within Pantheon+, a truncation in magnitude produces a sharply truncated redshift distribution, whereas a truncation in redshift yields a small tail toward higher magnitudes. We therefore regard SN magnitude selection as marginally more likely and adopt it as our fiducial scenario.
• Figure 2: Directed acyclic graph of the probabilistic model used to forward model the Cepheid magnitudes and the host galaxy redshifts. The left-hand dashed black box delineates the portion of the model used to constrain $H_0$. Excluding it yields the analysis in \ref{['sec:Cepheid_only_distances']}, where we infer Cepheid host galaxy distances using only the CPLR and the two geometric anchors (LMC and NGC 4258). See \ref{['sec:method_selection_function']} for details on our modelling of sample selection. The dashed black box on the right marks the SN magnitude selection, for which we sample $M_B$ and forward-model the supernova apparent magnitudes to model the selection. When assuming redshift selection for the host sample, this step is omitted.
• Figure 3: The expected peculiar velocity correlation coefficients computed from the LCDM peculiar velocity covariance matrix (see \ref{['sec:LCDM_covariance']}) for the 35 Cepheid host galaxies. A large fraction of the peculiar velocities are strongly correlated, reducing the effective sample size and highlighting the need for a local Universe reconstruction such as Carrick_2015.
• Figure 4: Corner plot of the inferred distance moduli to the LMC, NGC 4258, and the CPLR zero-point calibration, from analyses that do not incorporate redshift information. We compare four scenarios: a uniform-in-volume prior on host galaxy distances without selection modelling (blue), a uniform-in-distance-modulus prior without selection modelling (red), a uniform-in-volume prior with SN magnitude selection modelled (green), and a uniform-in-volume prior with Cepheid magnitude selection (violet). The uniform-in-distance-modulus prior agrees with the SH0ES analysis Riess_2022, which implicitly assumes this prior (black). The uniform-in-volume posteriors with either SN or Cepheid magnitude selection are in excellent agreement with the SH0ES calibration. Contours denote $1\sigma$ and $2\sigma$ confidence intervals.
• Figure 5: Comparison of distances to the 35 Cepheid host galaxies between a Cepheid-only distance inference using a uniform-in-volume prior without any selection (black), or with SN magnitude selection (blue), or with Cepheid magnitude selection (green) relative to a uniform-in-distance-modulus prior without selection modelling. The first yields an average distance shift of $0.045~\mathrm{mag}$ (which corresponds to $H_0$ being biased high by $1.79^{+1.00}_{-0.42}$ per cent), the second yields no systematic offset, whereas the third yields an average distance shift of $0.022~\mathrm{mag}$. The error bars represent $1\sigma$ uncertainties.