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Two per cent measurement of $H_0$ from Cepheids alone

By applying rigorous selection modeling and advanced density/peculiar velocity modeling to Cepheid data alone, this study derives a Hubble constant of $71.1 \pm 1.4~\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ , demonstrating that second-rung distance ladder measurements can achieve sufficient precision to meaningfully contribute to the ongoing Hubble tension debate.

Original authors: Richard Stiskalek, Harry Desmond, Eleni Tsaprazi, Alan Heavens, Guilhem Lavaux, Stuart McAlpine, Jens Jasche

Published 2026-06-11

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CC BY 4.0

Original authors: Richard Stiskalek, Harry Desmond, Eleni Tsaprazi, Alan Heavens, Guilhem Lavaux, Stuart McAlpine, Jens Jasche

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: The Universe's Speedometer is Broken

Imagine the universe is a giant car speeding away from us. Astronomers have two different ways to measure how fast this car is going (a value called the Hubble Constant, or $H_0$ ).

The "Baby Picture" Method: Looking at the Cosmic Microwave Background (the afterglow of the Big Bang) suggests the car is going about 67 km/s.
The "Local Trip" Method: Looking at nearby stars and exploding stars (supernovae) suggests the car is going about 73 km/s.

These two numbers don't match. This disagreement is called the "Hubble Tension." It's like if your GPS said you were driving 60 mph, but your speedometer said 70 mph. Something is wrong with the map, the car, or the instruments.

The Paper's Goal: Checking the "Local Trip"

This paper tries to fix the "Local Trip" measurement to see if the error is in the method itself.

Usually, the "Local Trip" method uses a three-step ladder:

Step 1: Measure distances to nearby stars in our galaxy (using parallax).
Step 2: Use those stars to calibrate Cepheid variables (pulsating stars that act like cosmic lighthouses) in nearby galaxies.
Step 3: Use those Cepheids to calibrate Supernovae (exploding stars) in faraway galaxies to measure the expansion speed.

The authors decided to skip Step 3. They wanted to see if they could get an accurate speed reading using only Step 1 and Step 2 (Cepheids and their host galaxies). They wanted to know: Is the discrepancy caused by the supernovae (Step 3), or is the problem even earlier in the ladder?

How They Did It: The "Smart Map" and the "Selection Filter"

To get a precise answer without the supernovae, the authors had to solve two tricky problems:

1. The "Moving Train" Problem (Peculiar Velocities)

Imagine you are trying to measure the speed of a train on a track, but the train is also on a moving platform. In space, galaxies aren't just moving away from us due to the expansion of the universe; they are also being tugged by the gravity of nearby massive clusters (like the Virgo Cluster). This is called peculiar velocity.

The Old Way: Previous studies treated these tugs as random noise or used simple, flat maps.
The New Way: The authors used a super-advanced, 3D "smart map" called Manticore-Local. Think of this as a high-definition, real-time weather forecast for gravity. It doesn't just guess where the wind is blowing; it reconstructs the actual flow of the "wind" (gravity) pulling on every single galaxy in their sample. This allowed them to subtract the "tugs" much more accurately than before.

2. The "Bouncer at the Club" Problem (Selection Effects)

The authors realized that the list of galaxies they were studying wasn't a random sample. It was like a VIP list for a club. The galaxies were chosen because they hosted a specific type of supernova that was bright enough to be seen.

The Mistake: If you only study the "VIPs" (bright supernovae) and pretend you studied everyone, your math will be wrong. You might think the club is smaller or the guests are closer than they really are.
The Fix: The authors built a mathematical model to account for the "bouncer." They asked: "If we had looked at every galaxy, not just the ones with bright supernovae, what would the data look like?" By correcting for this bias, they avoided a common trap that makes measurements look faster than they are.

The Results: A Slower, More Precise Speed

After applying their "smart map" and fixing the "bouncer" bias, they got a new result:

Their Result: 71.1 km/s (with a very small margin of error).
Comparison:
- This is lower than the previous "Local Trip" result (73 km/s).
- It is still higher than the "Baby Picture" result (67 km/s).
- The gap between their result and the "Baby Picture" is still significant (about 2.8 times the size of the error bar).

What does this mean?
Even when they removed the supernovae (Step 3) and used only the Cepheid stars (Step 2), the speed of the universe still didn't match the "Baby Picture." This suggests that the problem isn't just a mistake in the supernova data; the tension is real and likely requires new physics to explain.

The Takeaway

The authors proved that you can measure the universe's expansion speed with incredible precision (within 2%) using only the first two rungs of the distance ladder, provided you have a very good map of local gravity and a strict understanding of how the data was selected.

While they didn't solve the Hubble Tension (the numbers still don't match), they tightened the screws on the measurement, showing that the disagreement is robust and not just a calculation error. They essentially said, "We checked the math without the supernovae, and the mystery remains."

Technical Summary: Two per cent measurement of $H_0$ from Cepheids alone

Problem Statement
The persistence of the "Hubble tension"—a statistically significant discrepancy between the Hubble constant ( $H_0$ ) inferred from the Cosmic Microwave Background (CMB) under the $\Lambda$ CDM model ( $\sim 67.4$ km s $^{-1}$ Mpc $^{-1}$ ) and local distance ladder measurements ( $\sim 73.0$ km s $^{-1}$ Mpc $^{-1}$ )—remains a critical challenge in cosmology. A primary source of uncertainty in local measurements is the reliance on Type Ia Supernovae (SNe) for the third rung of the distance ladder, which introduces complex systematics related to standardization, dust correction, and selection effects. Previous attempts to infer $H_0$ using only the first two rungs (geometric anchors and Cepheids) have yielded results consistent with the full SH0ES analysis but with larger uncertainties and potential biases in selection modeling. This study revisits the "Cepheids alone" approach to determine if a precise, SN-independent measurement of $H_0$ is achievable and to assess whether the tension persists when SNe are removed from the inference pipeline.

Methodology
The authors construct a Bayesian forward model to infer $H_0$ using a two-rung distance ladder composed of:

Geometric Anchors: Parallax measurements from Gaia and HST for Milky Way Cepheids, detached eclipsing binaries in the Large Magellanic Cloud (LMC), and water masers in NGC 4258.
Cepheid Observables: Periods, apparent magnitudes, and metallicities for 3,130 Cepheids in 35 host galaxies (excluding the anchors).
Redshifts: Observed redshifts of the 35 Cepheid host galaxies (converted to the CMB frame).

Key methodological improvements over previous work (specifically Kenworthy et al. 2022, or K22) include:

Forward Modeling: Unlike K22, which used pre-computed distances, this study forward-models Cepheid observables directly in a single-step inference, treating host distances as latent variables.
Rigorous Selection Function Modeling: The authors explicitly model the sample selection process. They test two primary scenarios: selection based on SN apparent magnitude ( $m_{SN} \lesssim 14$ ) and selection based on host galaxy redshift ( $cz \lesssim 3300$ km s $^{-1}$ ). They derive a principled Bayesian framework to account for unobserved sources, avoiding ad-hoc modifications to distance priors. The SN magnitude selection is identified as the most plausible scenario based on distribution comparisons with the Pantheon+ sample.
State-of-the-Art Peculiar Velocity Modeling: The study employs the Manticore-Local reconstruction, a density and velocity field reconstruction of the local Universe derived from the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm. This provides posterior samples of the initial conditions, allowing for marginalization over reconstruction uncertainties and accurate modeling of non-linear flows and galaxy bias. This is contrasted with linear-theory reconstructions (Carrick et al. 2015) and simple diagonal covariance assumptions.
Prior Consistency: The analysis adopts a uniform-in-volume prior for host galaxy distances ( $p(r) \propto r^2$ ), correcting for the bias introduced by the uniform-in-distance-modulus prior used in previous analyses.

Key Contributions

Principled Selection Modeling: The paper demonstrates that neglecting selection effects or modeling them incorrectly (e.g., by modifying priors on latent distances rather than modeling detection probabilities) introduces significant biases in $H_0$ .
Manticore-Local Application: It applies the most accurate available local velocity field reconstruction to distance ladder inference, quantifying the reduction in uncertainty compared to linear reconstructions.
SN-Independent Constraint: It provides a robust constraint on $H_0$ that relies solely on Cepheid data and geometric anchors, decoupled from the standardization and systematics of Type Ia Supernovae.

Results
Using the fiducial model (Manticore-Local velocity reconstruction and SN magnitude selection), the authors infer:
$H_0 = 71.1 \pm 1.4 \text{ km s}^{-1} \text{ Mpc}^{-1}$

Comparison to SH0ES: This result is approximately $1.3\sigma$ lower than the full SH0ES value ( $73.2 \pm 0.9$ km s $^{-1}$ Mpc $^{-1}$ ) but remains consistent within uncertainties.
Comparison to CMB: The result is in $2.8\sigma$ tension with the latest combined CMB data (Planck, ACT, SPT).
Selection Sensitivity: If the sample is assumed to be selected solely by host redshift, the inferred value shifts to $H_0 = 72.5 \pm 1.4$ km s $^{-1}$ Mpc $^{-1}$ . The true value likely lies between these two extremes.
Uncertainty Reduction: The use of Manticore-Local reduces the uncertainty on $H_0$ by approximately 18% compared to using the Carrick et al. (2015) reconstruction in the SN magnitude selection scenario.
Prior Impact: The study confirms that using a uniform-in-distance-modulus prior (as in K22) biases $H_0$ high by roughly 1.6% compared to the physically motivated uniform-in-volume prior.

Significance
The paper claims that a measurement of $H_0$ with sufficient precision (better than 2%) to meaningfully weigh in on the Hubble tension is achievable using second-rung data (Cepheids) alone. The results suggest that the Hubble tension is not an artifact of the third rung (SNe) alone, as the tension persists even when SNe are removed from the analysis, provided that selection effects and peculiar velocities are modeled rigorously.

The authors emphasize that the precision of this measurement is heavily dependent on the fidelity of the peculiar velocity modeling and the correct treatment of selection functions. They conclude that while the Cepheid-only measurement is consistent with the full SH0ES ladder, the lower central value in the fiducial scenario underscores the importance of robust statistical modeling. The work highlights that future improvements in $H_0$ precision may come from incorporating more second-rung data and refining local Universe reconstructions, potentially offering a path to a sub-1% determination of $H_0$ independent of SNe systematics.