🔭 astrophysics

A sound-horizon-free measurement of the Hubble constant from DESI DR2 baryon acoustic oscillations using artificial neural networks

Using an artificial neural network approach to combine DESI DR2 BAO data with Type Ia supernovae and cosmic chronometers, this study presents a model-independent, sound-horizon-free measurement of $H_0 = 71.5 \pm 2.2$ km s $^{-1}$ Mpc $^{-1}$ , providing independent support for the Hubble tension by favoring a higher value than the Planck CMB inference.

Original authors: Gaurav N. Gadbail, Kazuharu Bamba

Published 2026-04-28

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Gaurav N. Gadbail, Kazuharu Bamba

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 Cosmic Speedometer Mystery: A New Way to Measure the Universe

Imagine you are trying to figure out how fast a group of cars is driving on a massive, invisible highway that stretches across the entire country.

There are two main groups of "detectives" trying to solve this.

The "Early Bird" Detectives: They look at old, blurry photos of the very beginning of the trip. Based on how the cars were bunched up at the start, they calculate the speed should be 67 mph.
The "Local" Detectives: They stand on the side of the road and watch the cars zoom past them right now. They calculate the speed is actually 73 mph.

This disagreement is what scientists call the "Hubble Tension." It’s a huge problem because if our math is right, the universe shouldn't be behaving this way. It’s like two different GPS systems giving you two different speeds for the same car.

The New Approach: The "No-Assumptions" Method

The paper you provided introduces a new way to settle this debate. Most scientists use "models"—which are like educated guesses or blueprints—to fill in the gaps where they don't have data. But if your blueprint is slightly wrong, your speed calculation will be wrong too.

The authors, Gadbail and Bamba, decided to throw away the blueprints. They used a method that is "model-independent" and "sound-horizon-free."

The Analogy: The Measuring Tape vs. The Blueprint

Old Method: Imagine trying to measure a room by looking at a blueprint and guessing the size of the walls. If the architect made a mistake, your measurement is wrong.
This New Method: Instead of using a blueprint, they use a "universal ruler" that doesn't rely on any pre-drawn lines. They combine three different "clues" from the universe:
1. Supernovae (The Flashlights): Distant exploding stars that act like cosmic lightbulbs.
2. Cosmic Chronometers (The Stopwatches): Using old galaxies to measure how much time has passed.
3. DESI BAO (The Cosmic Ripples): Using the leftover "echoes" of sound waves from the early universe.

By mathematically mixing these three clues together, the "errors" in each one cancel each other out, and the "assumptions" about how the universe started disappear.

The Secret Weapon: Artificial Intelligence (ANN)

To make sense of all this messy, scattered data, the researchers didn't use standard math formulas. Instead, they used an Artificial Neural Network (ANN)—a type of AI modeled after the human brain.

Think of the AI as a Master Artist. The data points (the stars and galaxies) are like scattered dots of paint on a canvas. Instead of drawing a straight line between them (which might be too simple) or following a pre-set pattern (which might be biased), the AI "learns" the shape of the data. It looks at the dots and figures out the smoothest, most natural curve that connects them.

The Result: Is the Tension Real?

When the researchers ran their AI through the latest data from the DESI (Dark Energy Spectroscopic Instrument), they got a result for the universe's expansion speed:

$H_0 = 71.5 \pm 2.2 \text{ km/s/Mpc}$

What does this mean in plain English?
It means the speed is closer to the 73 mph (the Local Detectives) than the 67 mph (the Early Bird Detectives).

The Big Takeaway:
Because this method didn't rely on any "blueprints" or "assumptions," this result is a heavy blow to the idea that the disagreement is just a math error. It provides strong, independent evidence that the Hubble Tension is real.

The universe is expanding faster than our standard theories predict, and we might need a whole new "rulebook" of physics to explain why.

Technical Summary: A Sound-Horizon-Free Measurement of $H_0$ from DESI DR2 BAO using Artificial Neural Networks

1. The Problem: The Hubble Tension

The "Hubble tension" is a fundamental discrepancy in modern cosmology regarding the present-day expansion rate of the universe ( $H_0$ ).

Early-Universe Probes: Measurements from the Cosmic Microwave Background (CMB), specifically the Planck 2020 results, favor a lower value ( $H_0 \approx 67.4 \text{ km s}^{-1}\text{ Mpc}^{-1}$ ) but are model-dependent, requiring the assumption of the $\Lambda$ CDM framework.
Local-Universe Probes: Measurements using the cosmic distance ladder (e.g., SH0ES via Cepheids) favor a higher value ( $H_0 \approx 73.04 \text{ km s}^{-1}\text{ Mpc}^{-1}$ ), creating a $5\sigma$ – $6\sigma$ tension.
The Gap: Existing methods often rely on either early-universe physics (sound horizon scale $r_d$ ) or local calibrations (absolute luminosity of SNe Ia), both of which introduce potential systematic biases or model dependencies.

2. Methodology: Model-Independent Reconstruction

The authors propose a completely data-driven, model-independent approach that bypasses both the sound horizon calibration and the absolute luminosity calibration of Type Ia Supernovae (SNe Ia).

A. Theoretical Framework (Distance Duality Relation):
The method utilizes the Distance Duality Relation (DDR), which states that in any metric theory of gravity, the luminosity distance $d_L(z)$ and angular diameter distance $d_A(z)$ are related by $d_L(z) = (1 + z)^2 d_A(z)$ . By combining three distinct probes, the authors derive a formula for $H_0$ where the sound horizon $r_d$ cancels out exactly:
$H_0 = \frac{\Xi_{\text{SNIa}}(z) H_{\text{CC}}(z)}{(1 + z)^2 \Xi_{\text{BAO}}(z)}$
Where:

$\Xi_{\text{SNIa}}(z) = H_0 d_L(z)$ (unanchored luminosity distance from SNe Ia).
$H_{\text{CC}}(z)$ (Hubble parameter from Cosmic Chronometers).
$\Xi_{\text{BAO}}(z) = H(z) d_A(z)$ (sound-horizon-free BAO combination).

B. Observational Datasets:

SNe Ia: Pantheon+ compilation (excluding Cepheid calibrators to avoid $H_0$ priors).
Cosmic Chronometers (CC): 32 measurements of differential aging in massive galaxies.
DESI DR2 BAO: Seven anisotropic tracers (LRG, ELG, QSO, and Ly $\alpha$ ) spanning $0.510 \leq z \leq 2.330$ .

C. Artificial Neural Network (ANN) Reconstruction:
Unlike previous studies that used Gaussian Process (GP) regression, this work employs an ANN reconstruction method.

Architecture: A single hidden layer with 4,096 neurons using the Exponential Linear Unit (ELU) activation function.
Advantage: ANN is a purely data-driven approach that does not require a fiducial cosmological model or a prior mean function, minimizing bias.
Uncertainty Quantification: A bootstrap procedure (1,000 realizations) is used. Each realization involves perturbing the data within its measurement uncertainties and re-training the network to capture the full propagation of errors through the non-linear mapping.

3. Key Contributions

Sound-Horizon-Free: The measurement does not require any knowledge of the sound horizon scale $r_d$ or CMB-based priors.
Luminosity-Independent: It does not require assumptions about the absolute magnitude ( $M_B$ ) of SNe Ia.
Advanced Reconstruction: Replaces GP with ANN, providing a more robust, model-independent function reconstruction.
Updated Data: Utilizes the latest DESI DR2 data, incorporating new tracers (ELG1 and QSO) that were unavailable in DR1.

4. Results

Joint Constraint: The study yields a joint measurement of $H_0 = 71.5 \pm 2.2 \text{ km s}^{-1}\text{ Mpc}^{-1}$ (at 68% confidence).
Comparison with Literature:
- Consistent with Local Probes: It is consistent with the TRGB ( $H_0 \approx 69.8$ ) and SH0ES ( $H_0 \approx 73.0$ ) results within $0.6\sigma$ .
- Tension with CMB: It remains in $\sim 2\sigma$ tension with the Planck 2020 result ( $H_0 \approx 67.4$ ).
Redshift Consistency: The individual $H_0$ estimates from the seven different BAO tracers are broadly consistent with one another, suggesting no significant redshift evolution of $H_0$ and supporting the cosmological principle.

5. Significance

This paper provides independent, empirical support for the reality of the Hubble tension. By removing the two most common "crutches" of cosmological measurement—the sound horizon and the SNe Ia calibration—the authors demonstrate that the discrepancy between early-universe and local-universe measurements persists even in a purely data-driven, model-free framework. This strengthens the argument that the tension may stem from new physics rather than systematic errors in standard calibrations.