Cosmic baryon census with fast radio bursts and gravitational waves

By unifying 104 localized fast radio bursts and 47 gravitational-wave events, this study presents an $H_0$-free measurement of the cosmic baryon density fraction ($\Omega_{\rm b} = 0.0488 \pm 0.0064$) that aligns with early-Universe observations and offers a robust late-Universe probe to address the $H_0$ tension and missing baryon problem.

The Gist

Here is an explanation of the paper "Cosmic baryon census with fast radio bursts and gravitational waves," translated into simple, everyday language with creative analogies.

The Big Mystery: Where is the Missing Stuff?

Imagine the Universe is a giant, invisible ocean. Scientists know exactly how much water (matter) should be in this ocean based on how the Universe began (the Big Bang). They call this "baryonic matter"—basically, the stuff that makes up stars, planets, and us.

However, when astronomers look at the local Universe (the neighborhood around us), they can only find about 70% of that water. The other 30% is missing. It's like baking a cake where you measured out the flour, sugar, and eggs, but when you taste the batter, it's missing a huge chunk of ingredients. This is known as the "Missing Baryon Problem."

Scientists suspect this missing stuff is hiding in a faint, hot gas that is too dim to see with normal telescopes. To find it, we need a new way to "weigh" the Universe.

The Two New Detectives: FRBs and Gravitational Waves

To solve this mystery, the authors of this paper recruited two brand-new cosmic detectives:

1. Fast Radio Bursts (FRBs): Think of these as cosmic lighthouses. They are incredibly bright, millisecond-long flashes of radio waves coming from deep space. As these flashes travel through the Universe to reach us, they pass through the invisible gas. The gas slows down the radio waves slightly, just like running through water makes you slower than running through air.

   • The Clue: By measuring how much the signal got "slowed down" (called Dispersion Measure), scientists can calculate how much gas the signal passed through. This tells us how much "missing matter" is out there.

2. Gravitational Waves (GWs): Think of these as ripples in a pond caused by massive objects crashing together (like black holes). Unlike light, these ripples don't get slowed down by gas. Instead, they tell us exactly how far away the crash happened.

   • The Clue: These ripples act as "Standard Sirens." Just like you can tell how loud a siren is from a distance, scientists can tell exactly how far away the crash is just by looking at the shape of the wave. This gives them a precise distance measurement.

The Problem: The "Hubble Tension" (The Ruler is Broken)

Here is the tricky part. To figure out how much gas is in the Universe using the FRBs, you need to know how fast the Universe is expanding (the Hubble Constant, or $H_0$).

Imagine you are trying to measure the length of a room using a tape measure. But, you don't know if your tape measure is stretched out or shrunk.

• One group of scientists says the tape measure is length X (Early Universe measurements).
• Another group says it's length Y (Late Universe measurements).
• They disagree by a significant amount. This is called the "Hubble Tension."

If you use the wrong length for your tape measure, your calculation of the "missing gas" will be wrong. Previous studies tried to guess the tape measure's length, which could have biased their results.

The Solution: A Self-Checking System

This paper is brilliant because it doesn't guess the tape measure's length. Instead, it uses both detectives together to solve the puzzle without needing to know the expansion rate beforehand.

• FRBs tell us about the amount of gas (the missing matter).
• Gravitational Waves tell us the distance (which helps fix the expansion rate).

It's like having a scale and a ruler that talk to each other. If you know the weight of an object and its size, you can figure out its density without needing to know the exact temperature of the room.

By combining 104 FRBs (the lighthouses) and 47 Gravitational Wave events (the ripples), the scientists created a "self-calibrating" system.

The Results: The Case is Closed (Mostly)

When they put all the data together, they found:

1. The Missing Matter is Found: They calculated that the total amount of normal matter in the Universe is 0.0488 (a specific fraction). This matches perfectly with what we saw in the very early Universe (from the Big Bang).
2. The Tape Measure is Fixed: They also calculated the expansion rate of the Universe ($H_0$) to be about 71.6. This is right in the middle of the two conflicting groups, offering a fresh, independent perspective.

Why This Matters

Think of this like solving a jigsaw puzzle where two pieces were missing.

• Old way: We tried to guess what the missing pieces looked like based on the picture on the box (which was blurry).
• New way: We found the actual missing pieces (FRBs and Gravitational Waves) and snapped them into place.

The result is a "baryon census" (a headcount of all the matter) that is independent of the old arguments about how fast the Universe is expanding. It proves that the missing 30% of the Universe is likely just hiding in that faint, hot gas, and our understanding of the Big Bang is correct.

The Future

Currently, the "detectives" are a bit tired because we haven't seen enough of them yet (the sample size is small). But, as new telescopes come online, we will soon have thousands of FRBs and hundreds of gravitational wave events. This partnership will become the gold standard for measuring the Universe, finally settling the debate on where all our cosmic ingredients went.

Technical Summary

Here is a detailed technical summary of the paper "Cosmic baryon census with fast radio bursts and gravitational waves" by Ji-Guo Zhang et al.

1. Problem Statement

The paper addresses two critical issues in modern cosmology:

• The "Missing Baryon" Problem: While the Cosmic Microwave Background (CMB) and Big Bang Nucleosynthesis (BBN) precisely predict the baryon density of the early Universe ($\Omega_b$), approximately 30% of these baryons remain undetected in the local (late) Universe. They are hypothesized to reside in diffuse ionized gas (the Warm-Hot Intergalactic Medium, WHIM) that is too faint for direct observation.
• The $H_0$ Tension and Parameter Degeneracy: Fast Radio Bursts (FRBs) offer a promising method to trace these missing baryons via their Dispersion Measures (DM). However, the relationship between DM and redshift (the Macquart relation) involves a strong degeneracy between the baryon density ($\Omega_b$), the Hubble constant ($H_0$), and the fraction of baryons in the intergalactic medium ($f_d$).
  • Previous studies (e.g., Macquart20, Yang22) estimated $\Omega_b$ by fixing $H_0$ to specific values (e.g., 70 km s$^{-1}$ Mpc$^{-1}$) or using priors from early-Universe data (Planck) or late-Universe data (SH0ES).
  • Given the significant discrepancy ($>5\sigma$) between early and late-Universe $H_0$ measurements, fixing $H_0$ introduces systematic biases into the baryon census. A method is needed to measure $\Omega_b$ independently of $H_0$ assumptions.

2. Methodology

The authors propose a unified framework combining two independent late-Universe probes: Fast Radio Bursts (FRBs) and Gravitational Waves (GWs).

• Data Samples:

  • FRBs: 104 localized FRBs with measured redshifts. The sample was filtered to ensure the Milky Way contribution to DM is $<40\%$ and the extragalactic DM is $>80$ pc cm$^{-3}$.
  • GWs: 47 GW standard siren events from the GWTC-3 catalog (LIGO/Virgo/KAGRA), including 42 Binary Black Holes (BBHs), 3 Neutron Star-Black Holes (NSBHs), and 2 Binary Neutron Stars (BNSs). Redshifts for events without electromagnetic counterparts were inferred using the "dark siren" method (cross-matching with galaxy catalogs like GLADE+).

• Physical Modeling:

  • FRB DM Decomposition: The observed DM is modeled as the sum of Milky Way ISM, Milky Way halo, Intergalactic Medium (IGM), and host galaxy contributions.
    • The IGM contribution follows the Macquart relation, which links $\langle DM_{IGM} \rangle$ to $\Omega_b$, $H_0$, and $f_d$.
    • Statistical distributions are assigned to the halo, host, and IGM fluctuations (using hydrodynamic simulation priors like IllustrisTNG for IGM inhomogeneity).
  • GW Standard Sirens: GWs provide absolute luminosity distances ($D_L$) directly from waveform amplitudes. Since $D_L \propto 1/H_0$, GWs provide an independent, self-calibrated measurement of $H_0$ without relying on the cosmic distance ladder.

• Statistical Analysis:

  • A joint Markov Chain Monte Carlo (MCMC) analysis was performed using the bilby and emcee packages.
  • Likelihood: The total likelihood is the product of the FRB likelihood ($L_{FRB}$) and the GW likelihood ($L_{GW}$).
  • Parameters: The analysis simultaneously constrains cosmological parameters ($\Omega_b, H_0, \Omega_m$) and nuisance parameters (IGM fraction $f_d$, feedback parameter $F$, host DM properties $\mu_{host}, \sigma_{host}$, and GW population parameters).
  • Priors: Flat priors were used for $\Omega_b$, $H_0$, and other nuisance parameters. The authors tested robustness by varying the $\Omega_m$ prior and allowing GW population model parameters to vary freely.

3. Key Contributions

• First $H_0$-Free Baryon Census: This is the first study to derive the cosmic baryon density fraction ($\Omega_b$) at low redshift without assuming a fixed value or external prior for the Hubble constant.
• Breaking the Degeneracy: By combining FRBs (sensitive to $\Omega_b$) and GWs (sensitive to $H_0$), the strong $\Omega_b$-$H_0$ degeneracy inherent in FRB-only analyses is broken. The GW data anchors the $H_0$ measurement, allowing for a direct inference of $\Omega_b$.
• Unified Late-Universe Probe: The study establishes a novel paradigm where FRBs and GWs act synergistically to probe low-redshift cosmology, independent of early-Universe constraints (CMB/BBN) and the local distance ladder.

4. Key Results

• Baryon Density ($\Omega_b$):
  • The joint analysis yields $\Omega_b = 0.0488 \pm 0.0064$ (1$\sigma$).
  • This result is in excellent concordance with early-Universe predictions from CMB + BBN ($\sim 13\%$ precision).
  • This confirms that the "missing baryons" are indeed present in the local Universe, likely in the form of diffuse ionized gas, resolving the missing baryon problem within current uncertainties.
• Hubble Constant ($H_0$):
  • The joint constraint yields $H_0 = 71.6^{+4.4}_{-8.6}$ km s$^{-1}$ Mpc$^{-1}$.
  • This value is driven primarily by the GW data (which alone gives $H_0 \approx 72.6$) and sits between the Planck18 ($\sim 67.4$) and SH0ES ($\sim 73.0$) values, though the large error bars prevent a definitive resolution of the $H_0$ tension at this stage.
• Nuisance Parameters:
  • The analysis constrained the IGM baryon fraction to $f_d = 0.90 \pm 0.04$, indicating that $\sim 90\%$ of baryons in the IGM are in the diffuse ionized phase.
  • Host galaxy DM properties were also constrained, consistent with previous estimates.
• Robustness Checks:
  • Varying the GW population model parameters (freeing $\mu_g$) shifted the results slightly ($\Omega_b \approx 0.045$) but remained consistent with CMB+BBN at the 1$\sigma$ level.
  • Relaxing the $\Omega_m$ prior also resulted in consistent values, though the analysis showed moderate dependence on the $\Omega_m$ prior, suggesting future larger samples will be needed to fully decouple these parameters.

5. Significance

• Validation of the Missing Baryon Hypothesis: The study provides strong, independent evidence that the missing baryons are accounted for in the local Universe, validating the theoretical models of the WHIM.
• New Cosmological Probe: It demonstrates the power of multi-messenger cosmology. The synergy between FRBs (probing matter distribution) and GWs (probing expansion rate) offers a robust, self-consistent way to measure fundamental cosmological parameters without relying on early-Universe assumptions.
• Future Outlook: While current precision is limited by sample size (104 FRBs, 47 GWs), the authors project that upcoming surveys (e.g., CHIME/Outriggers, DSA-110, and future LVK runs) will provide thousands of localized FRBs and hundreds of GW events. This will significantly tighten constraints, potentially resolving the $H_0$ tension and providing a high-precision census of the cosmic baryon budget.