🔭 astrophysics

Calibrating baryonic feedback with weak lensing and fast radio bursts

This paper proposes that cross-correlating Fast Radio Burst dispersion measures with weak gravitational lensing data from surveys like Euclid can significantly tighten constraints on baryonic feedback and neutrino masses, reducing uncertainties by a factor of five with approximately 50,000 FRBs.

Original authors: Robert Reischke, Dennis Neumann, Klara Antonia Bertmann, Steffen Hagstotz, Hendrik Hildebrandt

Published 2026-03-24

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CC BY 4.0

Original authors: Robert Reischke, Dennis Neumann, Klara Antonia Bertmann, Steffen Hagstotz, Hendrik Hildebrandt

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 as a giant, invisible ocean. Most of this ocean is made of "dark matter"—a mysterious, invisible substance that holds galaxies together. But there's also a smaller amount of "normal" matter (baryons), like gas and stars, which is the stuff we can actually see.

The problem is that this normal matter is messy. It gets heated up by exploding stars and super-massive black holes, then blown away like smoke from a fire. Scientists call this "baryonic feedback."

Here is the trouble: When we try to map the invisible dark matter ocean using Weak Lensing (a technique that looks at how gravity bends light from distant galaxies), this "smoke" from the feedback messes up our map. It's like trying to see the shape of a fish tank through a window that has been fogged up by steam. The steam (feedback) changes the view so much that we can't tell if the fish (dark matter) are moving because of the water's natural currents or because of the steam.

The New Tool: Fast Radio Bursts (FRBs)

The authors of this paper propose a new way to clear the fog. They suggest using Fast Radio Bursts (FRBs).

Think of an FRB as a cosmic "ping" or a flash of radio light that happens somewhere far away in the universe. As this radio signal travels across the cosmos to reach our telescopes, it has to swim through the "smoke" (the gas and electrons) of the universe.

The Analogy: Imagine running through a crowd. If you run through a dense crowd, you get slowed down and arrive late. If you run through an empty hallway, you arrive on time.
The Science: The radio signal from an FRB gets delayed by the electrons it hits. The more electrons it hits, the more it gets delayed. By measuring exactly how much the signal is delayed (called the Dispersion Measure), we can calculate exactly how much "smoke" (baryonic matter) is in the path.

The Big Idea: Two Eyes on the Problem

Currently, we only have one eye looking at the universe: Weak Lensing. It sees the total mass (Dark Matter + Normal Matter), but it gets confused by the "smoke."

The authors suggest we open a second eye: FRBs.

Weak Lensing sees the total weight of the universe.
FRBs see only the "smoke" (the electrons/baryons).

By comparing these two views, we can finally separate the "smoke" from the "water." It's like looking at a painting through a foggy window (Weak Lensing) while simultaneously holding a flashlight that only illuminates the fog (FRBs). Once you know exactly where the fog is, you can mathematically subtract it to see the painting clearly.

What Did They Find?

The team ran computer simulations to see how well this would work for future telescopes like Euclid and the Square Kilometre Array (SKA).

The Magic Number: They found that if we can detect about 50,000 FRBs (which is a very realistic goal for the next decade), we can clear up the "fog" of baryonic feedback incredibly well.
The Result: Adding FRBs to the mix makes our measurements of the universe's structure five times more precise regarding the "smoke" (feedback) than using Weak Lensing alone.
Bonus Discovery: Because we can now measure the "smoke" so accurately, we can also weigh the neutrinos (tiny, ghost-like particles) much better. The precision on the total mass of neutrinos improves by about 50%.

Why Does This Matter?

For a long time, scientists have been stuck. They know the "smoke" (feedback) is messing up their maps of the universe, but they didn't have a good way to measure the smoke itself without relying on complex computer guesses.

This paper says: "Stop guessing. Let's measure the smoke directly with FRBs."

It's a game-changer. It allows us to use the next generation of massive telescopes to their full potential, helping us answer big questions like:

How heavy are neutrinos?
Is the universe expanding faster than we thought?
What is the true shape of the cosmic web?

In short, FRBs are the new "fog lights" that will let us see the true shape of the universe, finally cutting through the confusion caused by exploding stars and black holes.

1. Problem Statement

Future Stage-4 large-scale structure (LSS) surveys (e.g., Euclid, LSST-Rubin, Roman) aim to constrain cosmological parameters by measuring the matter distribution on non-linear scales ( $k > 1 \, \text{Mpc}^{-1}h$ ). However, the interpretation of these measurements is severely limited by baryonic feedback (BF) processes.

The Challenge: Astrophysical processes such as star formation, supernovae, and Active Galactic Nuclei (AGN) displace baryons, altering the total matter power spectrum. These effects are highly non-linear and difficult to model analytically, relying instead on hydrodynamical simulations with sub-grid models.
The Consequence: Uncertainties in baryonic feedback create degeneracies with key cosmological parameters, particularly the sum of neutrino masses ( $\sum m_\nu$ ) and the amplitude of matter fluctuations ( $\sigma_8$ ).
Current Limitations: Existing methods to constrain baryons, such as the thermal (tSZ) and kinetic (kSZ) Sunyaev-Zel'dovich effects, are limited by specific systematics and redshift weighting. There is a need for an independent probe of the electron distribution to break these degeneracies.

2. Methodology

The authors propose a joint analysis combining Cosmic Shear (weak gravitational lensing) and Fast Radio Burst (FRB) dispersion measures to constrain baryonic feedback.

A. Probes

Cosmic Shear: Measures the projected total matter distribution (dominated by dark matter) via the distortion of background galaxy shapes. It is sensitive to the total matter power spectrum $P_{\delta\delta}$ .
FRB Dispersion Measure (DM): FRBs are extragalactic radio transients. As their signals travel through the ionized intergalactic medium (IGM), they experience a frequency-dependent delay proportional to the integrated free electron density along the line of sight.
- The DM is decomposed into contributions from the Milky Way, the host galaxy, and the LSS ( $D_{\text{LSS}}$ ).
- $D_{\text{LSS}}$ is directly proportional to the electron density, which traces the baryonic distribution.
- The authors model the electron density as $n_e \propto \bar{\rho}_b [1 + b_e \delta_m]$ , where $b_e$ is the electron bias.

B. Statistical Framework

Power Spectra: The authors calculate the angular power spectra for:
- DM auto-correlation ( $C_{DD}$ ).
- Cosmic shear auto-correlation ( $C_{\gamma\gamma}$ ).
- Cross-correlation between DM and shear ( $C_{D\gamma}$ ).
Noise Modeling:
- Shear: Dominated by intrinsic shape noise ( $\sigma_\epsilon$ ).
- FRB: Dominated by "field noise" (cosmic variance of the electron density) and "host noise" (scatter from the host galaxy contribution, $\sigma_{\text{host}}$ ).
Feedback Model: They utilize HMcode (via pyhmcode) to model the matter power spectrum. Baryonic feedback is controlled by a single nuisance parameter, $\log_{10} T_{\text{AGN}}$ , which represents the temperature of AGN heating.
Analysis Techniques:
- Fisher Matrix Forecast: To estimate parameter constraints for a Stage-4 survey (Euclid-like) combined with an FRB sample ( $N_{\text{FRB}} = 5 \times 10^4$ ).
- MCMC (Markov Chain Monte Carlo): To validate constraints using a noiseless data vector with flat priors on cosmological parameters.

C. Survey Specifications

FRB Sample: $5 \times 10^4$ events with a redshift distribution $n(z) \propto z^2 e^{-z^{3.5}}$ .
Lensing Survey: Modeled after Euclid (0.3 sky fraction, 30 arcmin $^{-2}$ source density, 10 tomographic bins).
Overlap: The analysis assumes complete overlap of the survey footprints to maximize cross-correlation signal.

3. Key Contributions

Novel Probe Combination: This is the first study to propose using the statistical properties of FRB Dispersion Measures (specifically angular correlations) to calibrate baryonic feedback in conjunction with weak lensing.
Breaking Degeneracies: The authors demonstrate that while cosmic shear is sensitive to the total matter distribution, FRB DM is sensitive to the baryonic (electron) distribution. Since baryons are more strongly affected by feedback than dark matter, combining these probes breaks the degeneracy between feedback parameters and cosmological parameters.
Quantitative Constraints: The paper provides specific forecasts showing that FRBs can significantly tighten constraints on feedback models, which in turn improves constraints on neutrino masses.

4. Results

The analysis yields the following quantitative findings (based on $5 \times 10^4$ FRBs and Euclid-like shear data):

Baryonic Feedback ( $\log_{10} T_{\text{AGN}}$ ):
- Cosmic shear alone constrains the feedback parameter with an uncertainty of $\sim 0.24$ .
- Adding FRBs improves this constraint by a factor of ~5 (reducing uncertainty to $\sim 0.048$ in MCMC analysis, or an order of magnitude improvement in Fisher analysis).
- This represents a roughly 400-500% improvement in precision.
Neutrino Mass ( $\sum m_\nu$ ):
- Due to the degeneracy between neutrino mass and feedback, the improved feedback constraints translate to better neutrino mass limits.
- The uncertainty on $\sum m_\nu$ improves by ~25-50% (from $\sim 0.36$ eV to $\sim 0.27$ eV).
Other Parameters:
- Hubble Constant ( $h$ ) and Baryon Density ( $\Omega_b$ ): FRBs provide strong constraints on these parameters (improving by factors of ~10-100 compared to shear alone) because they directly scale the DM amplitude.
- Primordial Slope ( $n_s$ ): FRBs help break the degeneracy between $n_s$ and feedback, improving constraints by ~43%.
Signal-to-Noise Ratio (SNR):
- The cumulative SNR for the FRB sample alone is $\sim 100$ .
- The Euclid shear SNR is $\sim 1000$ .
- The cross-correlation adds significant signal power, particularly at multipoles $\ell \sim 100$ , where the feedback effects are most distinct.

5. Significance and Conclusion

Independent Calibration: FRBs offer a completely independent probe of the baryon distribution compared to tSZ/kSZ or X-ray observations. They rely on different systematics and have a different redshift weighting function, making them ideal for cross-checking and calibrating feedback models.
Feasibility: The required sample size ( $5 \times 10^4$ FRBs) is achievable within the next decade by upcoming facilities like SKA, DSA-2000, or CHORD.
Impact on Cosmology: By effectively calibrating baryonic feedback, this method unlocks the full potential of Stage-4 LSS surveys to measure the sum of neutrino masses and test modified gravity theories, which are currently limited by theoretical uncertainties in baryonic physics.
Future Work: The authors note that current limitations include the use of a simple one-parameter feedback model and Gaussian statistics. Future work will address more complex feedback models and systematic effects, but the core finding—that FRB correlations are a powerful tool for baryonic calibration—remains robust.

In summary, the paper establishes that correlating FRB dispersion measures with weak lensing data is a highly effective strategy to disentangle baryonic feedback from cosmological parameters, significantly enhancing the scientific return of future cosmological surveys.