🔭 astrophysics

Constraints on the baryon density from fast radio bursts using a non-parametric reconstruction of the Hubble parameter

Using a non-parametric reconstruction of the Hubble parameter from cosmic chronometer data, this study analyzes 130 well-localized fast radio bursts to constrain the baryon density ( $\Omega_{\rm b}h^2$ ) and host galaxy contributions, finding results that align excellently with early-Universe constraints while demonstrating the potential of future FRB samples to achieve sub-percent precision.

Original authors: Lázaro L. Sales, Klecio E. L. de Farias, Amilcar R. Queiroz, Rafael A. Batista, Bruno W. Ribeiro, Raiff H. Santos

Published 2026-05-05

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CC BY 4.0

Original authors: Lázaro L. Sales, Klecio E. L. de Farias, Amilcar R. Queiroz, Rafael A. Batista, Bruno W. Ribeiro, Raiff H. Santos

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

Imagine the universe is a giant, invisible ocean, and the "water" in this ocean is made of ordinary matter (baryons) that we can see in stars and gas, plus a lot of invisible stuff floating around. Scientists have long tried to measure exactly how much of this "water" exists in the universe.

This paper is like a new, clever way to measure that water using Fast Radio Bursts (FRBs).

The Cosmic Ping Pong

Think of an FRB as a super-fast, super-bright flash of radio light sent from a distant galaxy. It's like a cosmic ping-pong ball shot across the universe. As this ball travels through the cosmic ocean, it hits invisible electrons (the "water").

When the ball hits these electrons, it slows down slightly. Lower-frequency waves slow down more than high-frequency waves. By the time the signal reaches our radio telescopes on Earth, it's "stretched out" or dispersed. The amount of stretching is called the Dispersion Measure (DM).

The more stretching there is, the more "water" (baryons) the signal had to pass through. So, in theory, if we measure the stretching, we can count the water.

The Problem: The Foggy Host

There's a catch. The signal doesn't just travel through the cosmic ocean; it also has to escape the galaxy where it was born (the "host galaxy"). This is like the signal having to swim through a thick, local fog before it even reaches the open ocean.

We don't know exactly how thick that local fog is for every single FRB. Some galaxies are foggy; some are clear. If we guess wrong about the fog, our calculation of the total ocean water will be wrong. This is the main "degeneracy" (a fancy word for a confusing mix-up) the scientists had to solve.

The Solution: A Non-Parametric Map

Usually, to calculate the distance the signal traveled, scientists assume a specific shape for the universe's expansion (like assuming the ocean is always expanding at a specific, predictable rate). But what if that assumption is slightly off?

Instead of guessing the shape of the universe, these authors used a Neural Network (a type of AI) to draw a map of the universe's expansion history directly from real data (called "cosmic chronometers").

The Analogy: Imagine trying to measure the speed of a car. Instead of assuming the car drives on a perfectly straight, flat road (a theoretical model), you use a drone to film the actual road, including all its bumps and curves, and measure the speed based on what you actually see.
The Tool: They used a tool called ReFANN to create this "drone footage" of the universe's expansion. This map was built independently of the FRBs, so it didn't bias the results.

The Experiment: Real Data vs. A Simulation

The team did two things:

The Real Test: They took 130 real FRBs that have been pinpointed to specific galaxies. They used their AI map to calculate the expansion history and then figured out the amount of "water" (baryon density) in the universe.
- The Result: They found a value that matches perfectly with what we learned from the very beginning of the universe (Big Bang Nucleosynthesis) and the Cosmic Microwave Background (Planck data). It's like measuring a river's flow today and finding it matches the flow rate calculated from the river's source 13 billion years ago. The match is so close it's only off by about 0.05%—essentially a perfect tie.
The Future Test (The Mock Catalog): They created a simulation of 2,000 fake FRBs to see what would happen if we had a much bigger sample size in the future.
- The Result: With this larger "virtual" sample, their measurement became incredibly precise (down to less than 1% uncertainty). This suggests that as we find more real FRBs, this method will become a top-tier tool for measuring the universe's ingredients.

What They Also Found

While counting the "water," they also figured out the "fog" (the host galaxy contribution).

They estimated the typical amount of dispersion caused by the host galaxy (the median).
They measured how much this fog varies from galaxy to galaxy (the scatter).
By measuring these at the same time as the water, they avoided the confusion that usually happens when you try to guess one without knowing the other.

The Bottom Line

This paper shows that Fast Radio Bursts are a powerful new tool for cosmology. By using AI to map the universe's expansion without making rigid theoretical assumptions, the scientists were able to count the universe's ordinary matter using signals from the "recent" universe (low redshift).

Their findings confirm that the amount of matter we see in the local universe today is exactly the same as what the Big Bang theory predicted existed at the dawn of time. It's a robust, independent check that says, "Our map of the universe is consistent, and our understanding of its ingredients is solid."

Technical Summary: Constraints on the Baryon Density from Fast Radio Bursts Using a Non-Parametric Reconstruction of the Hubble Parameter

Problem Statement
Fast Radio Bursts (FRBs) offer a unique pathway to measure the cosmic baryon density ( $\Omega_b h^2$ ) through their dispersion measure (DM), which accumulates as the signal traverses free electrons in the intergalactic medium (IGM). However, extracting precise cosmological constraints from FRB data is hindered by significant astrophysical uncertainties, primarily the contribution of the host galaxy ( $DM_{host}$ ). This contribution is typically modeled as a log-normal distribution characterized by a median ( $\tilde{\mu}$ ) and a logarithmic scatter ( $\sigma_{host}$ ), introducing degeneracies with $\Omega_b h^2$ and the background expansion history $H(z)$ . Furthermore, standard analyses often rely on specific cosmological models (e.g., $\Lambda$ CDM) to describe $H(z)$ , potentially biasing the inference of baryon density if the underlying model is incorrect. The current sample of well-localized FRBs with known redshifts remains limited, making it difficult to fully break these degeneracies without additional, model-independent information.

Methodology
To address these limitations, the authors employ a Bayesian inference framework that combines a sample of 130 well-localized FRBs with a non-parametric reconstruction of the Hubble parameter $H(z)$ .

Non-Parametric $H(z)$ Reconstruction: Instead of assuming a specific cosmological model, the authors utilize the ReFANN (Reconstruct Function with ANN) framework. This artificial neural network (ANN) is trained exclusively on cosmic chronometer (CC) data (35 measurements in the range $0.07 < z < 1.965$ ) to reconstruct the expansion history $H(z)$ . The network uses an Exponential Linear Unit (ELU) activation function and minimizes an absolute error loss function. This provides a model-independent $H(z)$ curve that is then incorporated into the theoretical calculation of the mean IGM dispersion measure, $\langle DM_{IGM}(z) \rangle$ .
Likelihood Construction: The analysis defines the likelihood based on the probability distribution of the extragalactic DM ( $DM_{ext}$ ). This distribution is derived by convolving the IGM contribution (modeled via the Macquart relation using the reconstructed $H(z)$ ) with a log-normal distribution representing the host galaxy contribution. The parameters to be constrained are the physical baryon density ( $\Omega_b h^2$ ), the median host contribution ( $\tilde{\mu}$ ), and the host scatter ( $\sigma_{host}$ ).
Bayesian Inference: Using nested sampling (MLFriends algorithm via the UltraNest package), the authors perform a joint inference of the three parameters using broad, uninformative priors. The analysis is conducted on two datasets:
- Real Data: A curated sample of 130 localized FRBs (excluding one physically inconsistent event, FRB 20220319D).
- Mock Catalog: A synthetic sample of 2,000 FRBs generated via Monte Carlo simulation. This mock catalog mimics CHIME telescope selection effects, incorporating intrinsic formation rates, luminosity functions, and redshift evolution, to forecast the potential of future large-scale surveys.

Key Results
The study yields the following constraints:

Real FRB Sample:
- $\Omega_b h^2 = 0.02236 \pm 0.00090$ (relative uncertainty $\sim 4\%$ ).
- Median host contribution $\tilde{\mu} = 178.15^{+16.51}_{-16.97}$ pc cm $^{-3}$ .
- Host scatter $\sigma_{host} = 0.794^{+0.064}_{-0.067}$ .
- The inferred $\Omega_b h^2$ is in excellent agreement with Big Bang Nucleosynthesis (BBN) and Planck CMB results, differing from their central values by only $\sim 0.05\%$ .
- The analysis reveals a moderate anti-correlation ( $r \simeq -0.43$ ) between $\Omega_b h^2$ and $\tilde{\mu}$ , reflecting the degeneracy where an increase in cosmological DM can be compensated by a decrease in the host contribution.
Mock Catalog (Forecast):
- $\Omega_b h^2 = 0.02248 \pm 0.00018$ (relative uncertainty $\sim 0.8\%$ ).
- $\tilde{\mu} = 182.36^{+6.83}_{-6.48}$ pc cm $^{-3}$ .
- $\sigma_{host} = 0.711^{+0.024}_{-0.025}$ .
- The mock analysis demonstrates that future samples of this magnitude could reduce uncertainties on $\Omega_b h^2$ to the sub-percent level, approaching the precision of early-Universe probes while remaining statistically consistent with BBN and Planck constraints.

Significance and Claims
The paper asserts that combining FRB dispersion measures with a non-parametric reconstruction of the expansion history provides a robust, model-independent pathway to constrain both cosmological and astrophysical parameters.

Consistency: The results validate FRBs as a complementary low-redshift probe of baryon density, showing full consistency with early-Universe determinations (BBN and Planck) without assuming a specific background cosmology.
Astrophysical Constraints: The study simultaneously constrains the host-galaxy distribution parameters ( $\tilde{\mu}$ and $\sigma_{host}$ ) more precisely than previous FRB-based estimates, which often fixed these values or relied on indirect estimators. The improved precision on $\sigma_{host}$ is highlighted as crucial for separating astrophysical and intergalactic contributions to the total DM.
Future Potential: The mock analysis illustrates that the current statistical limitations of FRB-only constraints are surmountable. With larger, better-characterized samples, FRBs can achieve precision comparable to CMB measurements, offering an independent check on the baryon density at low redshifts.

The authors conclude that their method effectively reduces model-driven degeneracies and establishes FRBs as a viable tool for precision cosmology, provided that future surveys can deliver larger samples and improved characterization of host environments.