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Consistent extinction model for type Ia supernovae in Cepheid-based calibration galaxies and its impact on $H_{0}$

By proposing a consistent extinction model that applies a uniform Milky Way-like $R_B$ distribution to all Cepheid-based calibration galaxies, this study corrects for systematic underestimations of supernova brightness in high-mass systems, resulting in a lower Hubble constant ( $H_0 = 70.5 \pm 1$ km/s/Mpc) that reduces the Hubble tension from $5.2\sigma$ to $2.8\sigma$ .

Original authors: Radosław Wojtak, Jens Hjorth

Published 2026-06-17

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CC BY 4.0

Original authors: Radosław Wojtak, Jens Hjorth

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 Picture: The Cosmic Speedometer Dispute

Imagine you are trying to measure how fast the universe is expanding. This speed is called the Hubble Constant ( $H_0$ ).

Currently, astronomers have two main ways to measure this speed, and they are disagreeing significantly:

The "Baby Universe" Method: Looking at the oldest light in the universe (the Cosmic Microwave Background). This suggests a slower expansion speed.
The "Local Universe" Method (SH0ES): Using a "cosmic distance ladder." This involves measuring distances to nearby stars (Cepheids) and then using exploding stars (Type Ia Supernovae) to measure distances to farther galaxies. This method suggests a faster expansion speed.

The difference between these two numbers is so large that it’s causing a major headache for physicists. It’s like one group of engineers says your car is going 60 mph, and another group says it’s going 75 mph. If the speedometer is wrong, we might need to rethink how the engine (the universe) works.

The Problem: Dirty Windshields and Wrong Wipers

The SH0ES team (led by Adam Riess) uses exploding stars (supernovae) as their primary measuring stick. But there’s a catch: Dust.

Space isn’t empty; it’s filled with cosmic dust that blocks and reddens the light from these exploding stars. To get an accurate distance, astronomers have to calculate how much light was blocked and "correct" for it. Think of it like trying to see a streetlight through a foggy windshield. You need to know how thick the fog is to judge how bright the light actually is.

The SH0ES team uses a computer model (called the P23 model) to estimate this dust. This model was trained on distant galaxies. It assumes that galaxies with lots of stars (high mass) have a specific type of dust, and galaxies with fewer stars (low mass) have a different type. Specifically, it assumes high-mass galaxies have "thinner" dust (a lower extinction coefficient, $R_B \approx 3$ ) compared to low-mass galaxies ( $R_B \approx 4$ ).

The Issue: The galaxies used to calibrate the distance ladder (the "calibration galaxies") are special. They are chosen because they are close enough for us to see individual stars (Cepheids). These galaxies tend to be disk-shaped and dusty, much like our own Milky Way.

The authors of this paper, Wojtak and Hjorth, argue that the SH0ES team is applying the wrong "wiper setting" to these calibration galaxies. By assuming the dust is "thinner" ( $R_B \approx 3$ ) in these massive, Milky Way-like galaxies, the model underestimates how much light is being blocked.

The Analogy: The Over-Optimistic Cleaner

Imagine you are cleaning windows.

The P23 Model is like a cleaning robot trained on office buildings. It learns that office windows usually have a light layer of dust.
The Calibration Galaxies are like residential houses with heavy pollen and dirt on the windows.

If you use the "office building" cleaning settings on the "residential house" windows, you won’t clean them thoroughly. You’ll think the window is cleaner than it actually is.

In astronomy terms: If you think the dust is thinner than it really is, you think the supernova is brighter than it really is. If you think the supernova is brighter, you calculate that it is closer than it really is. If the galaxies are closer than you think, the universe appears to be expanding faster than it really is.

The Solution: A Better Cleaning Model

The authors propose a simple fix. They suggest that for these specific calibration galaxies, we should stop using the "office building" dust model. Instead, we should use a "Milky Way-like" dust model.

They make two small changes:

Uniform Dust Type: They assume the dust in these galaxies is similar to our own Milky Way, regardless of the galaxy's mass. This means using a higher extinction coefficient ( $R_B \approx 4.3$ ), which accounts for thicker dust.
Better Dust Distribution: They tweak the mathematical shape of how the dust is distributed, ensuring the model fits the data better without changing the overall average amount of dust.

The Result: The Speedometer Slows Down

When they apply this new, more realistic "residential window" cleaning model to the data:

The supernovae appear dimmer (because they are now correctly accounting for more dust blocking the light).
Because they are dimmer, they are calculated to be farther away.
Because the galaxies are farther away, the calculated expansion speed of the universe slows down.

The Numbers:

Old SH0ES Result: $H_0 = 73.0$ km/s/Mpc (Fast)
New Result: $H_0 = 70.5$ km/s/Mpc (Slower)

Why This Matters

This new number ($70.5$) is much closer to the "Baby Universe" measurement ( $\approx 67-68$ ) and also matches another local measurement method called TRGB (Tip of the Red Giant Branch).

Before this fix, the disagreement between the two main methods was a massive 5.2 sigma (statistically, this is a huge, undeniable conflict). After the fix, the disagreement drops to 2.8 sigma.

While 2.8 sigma is still a tension (it’s not a perfect match), it is no longer a crisis that demands "new physics" or a rewrite of the laws of the universe. It suggests that the disagreement might just have been a measurement error caused by not accounting for the dust correctly, rather than a fundamental flaw in our understanding of cosmology.

Summary in a Nutshell

Conflict: Two methods of measuring the universe's expansion speed disagree.
Cause: The method using nearby exploding stars might be underestimating how much cosmic dust is blocking the light.
Fix: The authors updated the dust model to be more realistic for the specific galaxies used in the measurement.
Outcome: The calculated expansion speed slows down, reducing the conflict with other measurements. The "crisis" in cosmology is less severe than previously thought.

Technical Summary

Problem Statement
The paper addresses a systematic discrepancy in the determination of the Hubble constant ( $H_0$ ) using the SH0ES distance ladder, specifically regarding the treatment of dust extinction in Type Ia supernovae (SNe Ia) within Cepheid-based calibration galaxies. The SH0ES collaboration employs a probabilistic extinction model (Popovic et al. 2023, hereafter P23) trained on SNe Ia in the Hubble flow ( $z > 0.03$ ) and extrapolates it to the nearby calibration galaxies. The P23 model assumes different total-to-selective extinction coefficients ( $R_B$ ) based on host galaxy stellar mass: $\langle R_B \rangle \approx 3.1$ for high-mass galaxies ( $M_\star > 10^{10} M_\odot$ ) and $\langle R_B \rangle \approx 4.0$ for low-mass galaxies. The authors argue that this extrapolation is problematic because calibration galaxies are selected based on the presence of luminous Cepheids, biasing the sample toward late-type, dusty, disk-dominated systems. Consequently, the standard approach underestimates the brightness of reddened SNe Ia in high-mass calibration galaxies, leading to a potential bias in the derived $H_0$ .

Methodology
The authors analyze 42 distinct SNe Ia (77 measurements including duplicates) in 37 calibration galaxies using data from the Pantheon+ compilation and SH0ES Cepheid observations. They perform consistency tests by comparing the absolute magnitudes ( $M_B$ ) derived from SNe Ia in high-mass versus low-mass host galaxies against random control subsamples.

To resolve the identified systematic error, the authors propose a minimalistic modification to the extinction model applicable solely to the calibration galaxies, while retaining the P23 model for the Hubble flow. The new model involves two key changes:

Uniform $R_B$ Distribution: It adopts a Milky Way-like distribution for $R_B$ across all calibration galaxies, regardless of stellar mass, with a mean $\langle R_B \rangle = 4.3$ and scatter $\sigma_{R_B} = 0.4$ . This aligns the SN extinction correction with the extinction curve used for Cepheid color corrections.
Modified Reddening Distribution Shape: To preserve the effective slope ( $\beta \approx 3.0$ ) of the SN peak magnitude–color relation and the mean reddening $\langle E(B-V) \rangle$ established by the P23 model, the authors replace the exponential distribution of $E(B-V)$ with a Gamma distribution characterized by a shape parameter $\gamma = 3.44$ .

The authors recompute the bias corrections ( $\delta$ ) and floor uncertainties ( $\sigma_{floor}$ ) for the calibration sample using Monte Carlo simulations based on this new model. They then fit the calibration data and a joint fit of calibration and Hubble flow data to derive revised estimates for $M_B$ and $H_0$ .

Key Contributions

Identification of Systematic Bias: The paper demonstrates that the P23 model, when applied to calibration galaxies, yields systematically fainter absolute magnitudes for SNe Ia in high-mass hosts compared to low-mass hosts, a discrepancy not present in the Hubble flow training data.
Consistent Extinction Model: The proposed model reconciles the extinction corrections for SNe Ia with those for Cepheids in the same galaxies by adopting a consistent, Milky Way-like $R_B$ value.
Statistical Validation: The new model is shown to provide a significantly better fit to the calibration data than the standard P23 model, as quantified by the Bayesian Information Criterion (BIC).

Results

Consistency Tests: Under the standard P23 model, SNe Ia in high-mass calibration galaxies yield $H_0$ values that are $2.0\sigma$ (all SNe) and $2.3\sigma$ (red SNe, $c>0$ ) outliers compared to random subsamples. The new model alleviates this tension, bringing the high-mass subsample results within $0.7\sigma$ and $1.6\sigma$ of the control samples, respectively.
Model Comparison: The new extinction model is strongly favored over the P23 model for the calibration data, with a $\Delta \text{BIC} = -11.0$ . This improvement is driven by both better residuals ( $\Delta \chi^2_{min} = 8.4$ ) and a more accurate covariance matrix normalization ( $\Delta \ln \det C = 2.6$ ).
Hubble Constant: The revised analysis yields a best-fit Hubble constant of $H_0 = 70.5 \pm 1.0 \, \text{km s}^{-1} \text{Mpc}^{-1}$ . This represents a reduction of $2.9 \, \text{km s}^{-1} \text{Mpc}^{-1}$ from the SH0ES baseline value ( $73.4 \pm 1.0 \, \text{km s}^{-1} \text{Mpc}^{-1}$ ).
Tension Reduction: The new $H_0$ value reduces the tension with the Planck CMB-derived $H_0$ (assuming flat $\Lambda$ CDM) from $5.2\sigma$ to $2.8\sigma$ . The result is also consistent with the Tip of the Red Giant Branch (TRGB) based measurement by Freedman et al. (2019).

Significance
The paper claims that the discrepancy between Cepheid-based and TRGB-based $H_0$ measurements may be partially attributed to underestimated extinction in the Cepheid calibration galaxies. By demonstrating that a Milky Way-like extinction model provides a statistically superior fit to the calibration data and yields an $H_0$ consistent with alternative distance ladder methods, the authors suggest that the "mass-step" in extinction properties assumed in the P23 model may not apply uniformly to the specific subclass of late-type galaxies used for calibration. The work highlights the importance of ensuring that population properties of dust reddening and extinction in calibration samples match those in the Hubble flow training data to avoid systematic biases in cosmological parameter estimation.