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Cosmographic constraints from late-time probes including fast radio bursts

This study employs a model-independent cosmographic approach combining late-time probes, including fast radio bursts, baryon acoustic oscillations, supernovae, and cosmic chronometers, to derive precise constraints on cosmological parameters that suggest a potential late-time kinematic tension with the standard $\Lambda$ CDM model, particularly indicated by a jerk parameter significantly lower than unity.

Original authors: Lázaro L. Sales, Klecio E. L. de Farias, Amilcar R. Queiroz, João R. L. Santos, Rafael A. Batista, Ana R. M. Oliveira, Lucas F. Santana, Carlos A. Wuensche, Thyrso Villela, Jordany Vieira

Published 2026-01-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Lázaro L. Sales, Klecio E. L. de Farias, Amilcar R. Queiroz, João R. L. Santos, Rafael A. Batista, Ana R. M. Oliveira, Lucas F. Santana, Carlos A. Wuensche, Thyrso Villela, Jordany Vieira

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, expanding balloon. For decades, scientists have been trying to measure exactly how fast that balloon is inflating and whether the inflation is speeding up, slowing down, or changing its rhythm. This paper is a new attempt to measure that expansion using a fresh set of tools, including a mysterious cosmic phenomenon called "Fast Radio Bursts" (FRBs).

Here is a simple breakdown of what the researchers did and what they found, using everyday analogies.

The Mystery of the "Cosmic Ping"

First, let's talk about Fast Radio Bursts (FRBs).

The Analogy: Imagine you are standing on a beach and you hear a loud "ping" from a distant lighthouse. The sound of that ping travels through the air. If the air is thick with fog or dust, the sound gets muffled and delayed.
The Reality: FRBs are incredibly bright, millisecond-long flashes of radio waves coming from deep space. As they travel to Earth, they pass through a vast ocean of invisible gas (plasma) between galaxies. This gas slows down the lower-pitched radio waves more than the high-pitched ones. By measuring how much the signal gets "stretched out" or delayed, scientists can estimate how far the signal traveled and how much matter it passed through.

The Goal: Measuring the Universe Without a Map

Usually, to measure the Universe's expansion, scientists have to assume a specific "recipe" for what the Universe is made of (like how much dark energy or dark matter exists). This is like trying to calculate the speed of a car without knowing if it's carrying heavy cargo or just a driver.

This paper uses a method called Cosmography.

The Analogy: Instead of guessing the car's cargo, the researchers just look at the speedometer, the brake pedal, and the gas pedal directly. They don't care why the car is accelerating; they just measure how it is accelerating right now.
The Method: They used a mathematical "Taylor expansion" (a way of approximating curves) to describe the Universe's expansion using three key numbers:
1. $H_0$ (The Speed): How fast the Universe is expanding right now.
2. $q_0$ (The Brakes): Is the expansion slowing down or speeding up? (Negative means speeding up).
3. $j_0$ (The Jerk): Is the rate of that speeding up changing? (Like pressing the gas pedal harder or softer).

The Tools: A Team of Detectives

To get the best answer, the researchers didn't rely on just one tool. They combined four different "detectives":

FRBs: The new, mysterious radio pings.
Supernovae (SNe): Exploding stars that act as "standard candles" (known brightness) to measure distance.
DESI (BAO): A massive survey of galaxies that maps the "frozen sound waves" from the early Universe, acting like a cosmic ruler.
Cosmic Chronometers (CC): Old galaxies that act like clocks, telling us how fast time is passing relative to the expansion.

What They Found

The researchers ran a massive computer simulation (MCMC) to see which numbers fit all the data best.

1. The FRBs Alone:
When they used only the Fast Radio Bursts, they got a decent estimate for the expansion speed ( $H_0$ ), landing around 66.3. This is a bit lower than the value measured by the "SH0ES" team (who use nearby stars) but closer to the value measured by the "Planck" satellite (who look at the early Universe).

The Catch: FRBs alone weren't precise enough to tell if the Universe's expansion rhythm ( $j_0$ ) was behaving normally or strangely. They were like a blurry photo; you can see the shape, but not the details.

2. The "DESI + CMB" Team:
When they used the DESI galaxy survey combined with early Universe data (CMB), they got a very precise measurement of the expansion speed (65.6) and a very specific value for the "jerk" parameter ( $j_0$ ).

The Surprise: The "jerk" value they found was 0.58. In the standard model of physics ( $\Lambda$ CDM), this number should be 1.0. This suggests the Universe's expansion might be changing its rhythm in a way the standard model doesn't predict. It's like the car is suddenly easing off the gas pedal when it was supposed to keep accelerating.

3. The Grand Combination:
When they combined all four detectives (FRBs + Supernovae + DESI + Cosmic Clocks), the picture became incredibly sharp.

The Result: They pinned down the expansion speed to 68.0 with very high precision (less than 1% error).
The Tension: Even with all this data, the "jerk" parameter ( $j_0$ ) stayed low at 0.55. This reinforces the idea that there might be a "tension" or a disagreement between what we see in the local Universe (late-time) and what the standard model predicts. The DESI data seems to be the main driver of this low "jerk" value.

The Bottom Line

FRBs are the new kid on the block: They are useful and give results that agree with the "early Universe" measurements, but right now, they aren't precise enough to solve the mystery on their own. They are a helpful sidekick.
The Mystery Remains: The combination of all data suggests the Universe might be expanding in a way that doesn't quite fit our current "standard recipe" (specifically regarding the "jerk" parameter).
Future Hope: As we find more Fast Radio Bursts and get better data from new telescopes, these "cosmic pings" will become sharper tools, helping us solve whether the Universe is behaving exactly as we think it should, or if there is a new, hidden rule of physics at play.

In short: The researchers used a mix of exploding stars, galaxy maps, cosmic clocks, and radio bursts to measure the Universe's speed. They found a very precise speed, but the "acceleration pattern" they found is slightly weird, hinting that our current understanding of the Universe might need a tweak.

Technical Summary: Cosmographic Constraints from Late-Time Probes Including Fast Radio Bursts

Problem and Motivation
The paper addresses the ongoing "Hubble tension"—the discrepancy between early-Universe measurements of the Hubble constant ( $H_0$ ) derived from the Cosmic Microwave Background (CMB) and late-time measurements from the local distance ladder. Motivated by recent indications of deviations from the standard $\Lambda$ CDM model reported by the Dark Energy Spectroscopic Instrument (DESI) collaboration, the authors seek to investigate the late-time expansion history of the Universe using a model-independent approach. Specifically, they aim to constrain cosmographic parameters ( $H_0$ , the deceleration parameter $q_0$ , and the jerk parameter $j_0$ ) without assuming a specific cosmological model (e.g., $\Lambda$ CDM), relying instead on the Friedmann-Lemaître-Robertson-Walker (FLRW) metric and the cosmological principle. A primary focus is evaluating the utility of Fast Radio Bursts (FRBs) as a complementary probe in this context.

Methodology
The study employs a cosmographic approach, utilizing a Taylor series expansion of the scale factor $a(t)$ around the present time to express observables in terms of kinematic parameters up to the jerk term ( $j_0$ ). This method avoids assumptions regarding the energy composition of the Universe.

The analysis integrates four distinct late-time observational datasets:

Fast Radio Bursts (FRBs): A sample of 116 localized FRBs (reduced to 114 after applying a redshift mask $z < 1$ to ensure Taylor series convergence). The authors model the dispersion measure (DM) by separating contributions from the Milky Way, the host galaxy (modeled as a log-normal distribution), and the intergalactic medium (IGM, modeled via a quasi-Gaussian distribution based on the Macquart relation).
Supernovae (SNe): The Pantheon+SH0ES dataset containing 1,701 Type Ia supernova light curves (reduced to 1,563 for $z < 1$ ).
Baryon Acoustic Oscillations (BAO): DESI Data Release 2 (DR2) results, comprising 13 correlated measurements of $D_M/r_d$ , $D_H/r_d$ , and $D_V/r_d$ (reduced to 7 points for $z < 1$ ). To break the degeneracy between $H_0$ and the sound horizon $r_d$ , the authors apply a Gaussian prior on $r_d$ ( $147.09 \pm 0.26$ Mpc) inferred from Planck 2018 data under $\Lambda$ CDM assumptions. This combination is referred to as "DESI+CMB."
Cosmic Chronometers (CC): 35 differential age measurements (reduced to 27 for $z < 1$ ).

The authors utilize Bayesian inference via Markov Chain Monte Carlo (MCMC) analysis (using the UltraNest and GetDist packages) to estimate the posterior distributions of the parameters $\{H_0, q_0, j_0, \Omega_b h^2, \mu, \sigma_{host}, r_d, M_b\}$ . They perform individual analyses for each dataset and joint analyses combining all probes.

Key Contributions

FRB Integration: The paper provides a rigorous cosmographic analysis incorporating a sample of 116 localized FRBs, treating the host galaxy DM contribution as a free parameter with a log-normal distribution.
Model-Independent Constraints: It derives constraints on $H_0$ , $q_0$ , and $j_0$ without assuming a specific dark energy equation of state or matter density evolution, relying solely on kinematic expansions.
DESI DR2 Application: The study applies the latest DESI DR2 BAO data within a cosmographic framework, calibrated with Planck-inferred sound horizon values, to test for kinematic tensions.
Joint Analysis: It presents a comprehensive joint analysis combining FRBs, SNe, CC, and DESI+CMB to assess the synergistic impact on parameter precision and degeneracy breaking.

Results

FRB-Only Constraints: Using FRBs alone, the authors derive $H_0 = 66.35^{+4.13}_{-5.04}$ km s $^{-1}$ Mpc $^{-1}$ (precision $\sim$ 6%), $q_0 = -0.33^{+0.21}_{-0.15}$ , and $j_0 = 0.83^{+0.57}_{-0.67}$ . These results are consistent with the $\Lambda$ CDM expectation ( $j_0=1$ ) within $1\sigma$ but are incompatible with the SH0ES local measurement at $1\sigma$ , favoring the Planck value.
DESI+CMB Constraints: The DESI+CMB dataset yields $H_0 = 65.59^{+1.25}_{-1.24}$ km s $^{-1}$ Mpc $^{-1}$ ( $\sim$ 2% precision), $q_0 = -0.29^{+0.07}_{-0.08}$ , and $j_0 = 0.58^{+0.03}_{-0.04}$ . Notably, the jerk parameter $j_0$ is lower than the $\Lambda$ CDM value of 1 at the $1\sigma$ level, suggesting a potential tension in the late-time kinematic sector under standard early-Universe assumptions for the sound horizon.
Joint Constraints: Combining all datasets (FRB + SNe + DESI+CMB + CC) tightens the constraints significantly:
- $H_0 = 68.03^{+0.53}_{-0.52}$ km s $^{-1}$ Mpc $^{-1}$ (0.76% precision).
- $q_0 = -0.41 \pm 0.02$ .
- $j_0 = 0.55 \pm 0.02$ .
  The joint result favors the Planck 2018 estimate over SH0ES and maintains the trend of $j_0 < 1$ .
Tension Analysis: The authors calculate tension metrics ( $T$ ) between datasets. A significant tension ( $\sim$ 4.1 $\sigma$ ) is found between SNe and DESI+CMB regarding $H_0$ . The joint analysis reduces uncertainties but the central values remain consistent with early-Universe inferences.

Significance and Claims
The paper concludes that the cosmographic approach with FRBs alone provides a competitive, model-independent constraint on $H_0$ that aligns with early-Universe measurements. However, the primary driver of the observed kinematic tension (specifically the low value of $j_0$ ) is the DESI+CMB dataset under the adopted sound horizon calibration.

The authors modestly claim that at the current level of observational precision, FRBs play a complementary role in cosmographic analysis. While FRBs alone cannot decisively determine higher-order parameters like $j_0$ due to large uncertainties, their inclusion in joint analyses helps break degeneracies and refine constraints. The paper emphasizes that the impact of FRBs is expected to increase as larger, more precise samples of well-localized events become available from current and future radio facilities (e.g., BINGO). The work serves as a proof-of-concept for using FRBs to probe the late-time expansion history independently of specific dark energy models.

The Mystery of the "Cosmic Ping"

The Goal: Measuring the Universe Without a Map

The Tools: A Team of Detectives

What They Found

The Bottom Line

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