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arxiv: 2603.18223 · v2 · submitted 2026-03-18 · 🌌 astro-ph.CO · astro-ph.HE

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· Lean Theorem

Gamma-Ray Bursts as an Independent High-Redshift Probe of Dark Energy

Maria Giovanna Dainotti , Aleksander {\L}ukasz Lenart , Biagio De Simone , William Giar\`e , Eleonora Di Valentino , Dieter H. Hartmann , Nissim Fraija , Kazunari Iwasaki
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Gaetano Lambiase
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Pith reviewed 2026-05-15 08:33 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.HE
keywords gamma-ray burstsdark energyDainotti relationscosmological forecastshigh-redshift probeswCDMequation of state
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The pith

Gamma-ray bursts with plateau phases can constrain the dark energy equation of state to a precision comparable to Planck using samples of around 66 events.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that gamma-ray bursts observed up to redshift 9.2 can fill the gap between supernovae and the cosmic microwave background as a probe of dark energy. By using simulations based on the Dainotti relations for X-ray and optical plateaus, it forecasts that samples of several tens to hundreds of GRBs can achieve precision on the dark energy parameter w similar to current CMB data. A specific sample of about 66 optical GRBs reaches sigma_w of approximately 0.47 in the wCDM model. This is valuable because it provides an independent test of possible dynamical dark energy suggested by recent observations like DESI BAO. Machine learning techniques that infer redshifts can help reach these sample sizes sooner.

Core claim

Our results show that GRB samples containing several tens to hundreds of well-characterized plateau can already approach the precision currently achieved by CMB measurements on the Dark Energy equation-of-state parameter w. Particularly, a sample of ∼66 optical GRBs can reach a precision σ_w ≈ 0.47, comparable to that obtained from Planck within the wCDM framework. Using simulated GRB samples from the observed population and the two-dimensional Dainotti relations, these forecasts indicate that GRBs will serve as an independent high-redshift probe to test deviations from ΛCDM.

What carries the argument

The two-dimensional Dainotti relations between the luminosity at the end of the plateau phase and its rest-frame duration in X-ray and optical observations.

Load-bearing premise

The two-dimensional Dainotti relations remain valid and unbiased when extrapolated to high redshifts up to z=9.2 without significant selection effects or evolution in the GRB population.

What would settle it

Observing a sample of high-redshift GRBs where the measured plateau luminosity-duration correlation deviates from the low-redshift calibration by more than the expected scatter would falsify the forecasted precision.

Figures

Figures reproduced from arXiv: 2603.18223 by Aleksander {\L}ukasz Lenart, Biagio De Simone, Dieter H. Hartmann, Eleonora Di Valentino, Gaetano Lambiase, Kazunari Iwasaki, Maria Giovanna Dainotti, Nissim Fraija, William Giar\`e.

Figure 1
Figure 1. Figure 1: Left: The uncertainty on w derived with mock samples of 2300 GRBs simulated based on the Ntrimmed, the closest GRBs to the best-fit of the X-ray relation. The simulation was based on the varied a c σint parameters taken from the mean fit of the trimmed sample. Right: The same, but for the optical relation. With the sample described above, we have a starting point to obtain higher-precision cosmological con… view at source ↗
Figure 2
Figure 2. Figure 2: Uncertainty on the w parameter as a function of the GRB sample size used for computation. The blue continuous line is the uncertainty reached with Planck alone (left panel) and DESI alone (right panel). 5. RESULTS The results are divided into three parts: all of them deal with simulated GRB data. The first part presents the GRB analysis and evaluates the number of GRBs required to reach a precision compara… view at source ↗
Figure 3
Figure 3. Figure 3: Forecast constraints on w obtained from mock GRB samples. The first two rows correspond to the X-ray and optical correlations analysed with all cosmological parameters free to vary. The last two rows show the corresponding analyses with ΩM and H0 fixed. In each case we consider three calibration strategies for the GRB Dainotti 2D correlation: varying all correlation parameters (left column), fixing the nor… view at source ↗
Figure 4
Figure 4. Figure 4: 2D X-ray (top row) and optical (bottom row) mock GRBs analysed with the real Planck data. To assess the GRB+CMB constraining power in a more controlled forecasting setup, we therefore also consider simulated CMB data. Within the wCDM model, we assume a fiducial ΛCDM cosmology with w = −1 and generate mock CMB data using the public framework described in M. Rashkovetskyi et al. (2021). This allows us to iso… view at source ↗
Figure 5
Figure 5. Figure 5: 2D X-ray (top row) and optical (bottom row) mock GRBs analysed with simulated Planck data. All parameters of correlation fixed All parameters of correlation varied Normalization fixed 1000 1500 2000 2500 3000 3500 4000 0.2 0.4 0.6 0.8 1.0 1.2 N z -score Λ - w0 wa (a) Constrains obtained with X-ray sample. All parameters of correlation fixed All parameters of correlation varied Normalization fixed 1000 1500… view at source ↗
Figure 6
Figure 6. Figure 6: The z-score between ΛCDM and w0waCDM models computed with Equation 16. 2D mock GRBs are analysed with mock Planck data. we can estimate the probability of our best-fit being in disagreement with the ΛCDM model by computing a simple z-score: z = |wp, best−fit − wp, ΛCDM| σwp = |wp, best−fit + 1| σwp , (16) where σwp is the uncertainty on the wp parameter. In all our simulations, we obtained that the z incre… view at source ↗
Figure 7
Figure 7. Figure 7: Estimated total number of X-ray and optical GRB afterglow detections by current and possible future instruments as a function of years. 6.2. Future observations Currently, the majority of GRB X-ray afterglows are observed by the Swift satellite (N. Gehrels et al. 2004). However, the recent start of the SVOM (J. Wei et al. 2016) and Einstein Probe (W. Yuan et al. 2025a) missions and the development of plann… view at source ↗
Figure 8
Figure 8. Figure 8: Left: Estimated total number of X-ray GRB afterglow detections by current and possible future instruments as a function of year. Right: The same, but for optical detections. 7. SUMMARY, DISCUSSION AND CONCLUSIONS Our results have demonstrated the usefulness of GRBs as cosmological probes that complement traditional distance indicators, particularly by extending the exploration of the expansion history of t… view at source ↗
read the original abstract

Testing the $\Lambda$CDM model requires cosmological probes spanning the wide redshift interval between Type Ia Supernovae (SNe Ia, $z\lesssim2.9$) and the Cosmic Microwave Background (CMB, $z\approx1100$). Gamma-Ray Bursts (GRBs), observed up to redshift $z=9.2$, offer the opportunity to explore this regime. Here, we investigate how many GRBs are needed to become a useful cosmological probe capable of independently testing deviations from $\Lambda$CDM suggested by the recent DESI BAO observations. We develop forecasts based on the two-dimensional X-ray and optical Dainotti relations, between the luminosity at the end of the plateau phase and its rest-frame duration. Using simulated GRB samples constructed from the observed population, we evaluate the constraining power of GRBs on cosmological parameters within the $w$CDM and $w_0w_a$CDM models, both independently and in combination with CMB observations. Our results show that GRB samples containing several tens to hundreds of well-characterized plateau can already approach the precision currently achieved by CMB measurements on the Dark Energy (DE) equation-of-state parameter $w$. Particularly, a sample of $\sim66$ optical GRBs can reach a precision $\sigma_w \approx 0.47$, comparable to that obtained from Planck within the $w$CDM framework. Such sample sizes are already attainable through Machine Learning techniques that double the number of GRBs using inferred redshifts. These forecasts indicate that future GRB observations, when combined with next-generation transient missions and improved statistical techniques, will provide an independent high-redshift probe of cosmic expansion and will play an important role in testing the robustness of potential Dynamical DE signals suggested by other cosmological datasets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper develops forecasts for the constraining power of Gamma-Ray Bursts (GRBs) on dark energy parameters using simulated samples constructed from the observed population via the two-dimensional X-ray and optical Dainotti relations (luminosity at end of plateau vs. rest-frame duration). It claims that samples of several tens to hundreds of well-characterized GRBs can approach CMB-level precision on w, with a specific result that ~66 optical GRBs yield σ_w ≈ 0.47 in wCDM, comparable to Planck, and that such samples are already attainable via machine learning redshift inference; the forecasts are performed both standalone and in combination with CMB data in wCDM and w0waCDM models.

Significance. If the central forecasts hold, the work would establish GRBs as a viable independent high-redshift (up to z=9.2) cosmological probe capable of testing potential dynamical dark energy signals suggested by DESI BAO, bridging the gap between SNe Ia and CMB. The use of forward simulations from the observed GRB population (rather than fitting to target cosmological data) and the explicit sample-size thresholds provide concrete, falsifiable targets for future observations and machine-learning redshift techniques.

major comments (3)
  1. [Methods (simulation procedure)] The simulation procedure (described in the methods section on sample construction) assumes the 2D Dainotti relations fitted on the mostly low-z observed sample remain unbiased and unevolving when extrapolated to z up to 9.2; this assumption is load-bearing for the quoted σ_w ≈ 0.47 because any redshift-dependent change in slope, normalization, or scatter directly scales the simulated error budgets and Fisher-matrix constraints.
  2. [Results (Fisher forecasts)] The handling of selection effects and Malmquist bias in the simulated high-z catalogs is not validated with redshift-split tests or explicit evolution corrections; without these, the claimed precision for a sample of ~66 optical GRBs may be optimistic and the comparison to Planck wCDM results cannot be taken at face value.
  3. [§4 (cosmological parameter estimation)] The error propagation from the Dainotti relation parameters into the cosmological likelihood does not include marginalization over possible redshift evolution of the relation coefficients; this omission affects the standalone GRB constraints and their combination with CMB data.
minor comments (2)
  1. [Abstract] The abstract and introduction use 'several tens to hundreds' without a precise table linking sample size to σ_w; adding such a summary table would improve clarity.
  2. [Introduction] Notation for the plateau luminosity and duration in the Dainotti relations is introduced without an explicit equation reference in the first use; a numbered equation would aid readers.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We have carefully considered each point and provide point-by-point responses below. Where appropriate, we have revised the manuscript to address the concerns raised.

read point-by-point responses

  1. Referee: [Methods (simulation procedure)] The simulation procedure (described in the methods section on sample construction) assumes the 2D Dainotti relations fitted on the mostly low-z observed sample remain unbiased and unevolving when extrapolated to z up to 9.2; this assumption is load-bearing for the quoted σ_w ≈ 0.47 because any redshift-dependent change in slope, normalization, or scatter directly scales the simulated error budgets and Fisher-matrix constraints.

    Authors: We agree that the extrapolation of the Dainotti relations to high redshifts is a key assumption in our forecasts. The relations were calibrated using the available observed sample, which spans a range of redshifts up to z~9, though predominantly lower z. In the revised manuscript, we have expanded the methods section to explicitly discuss this assumption, including references to studies that have tested for redshift evolution in GRB relations and found no significant evidence within current uncertainties. We also added a sensitivity analysis showing how moderate evolution would impact the forecasted constraints, thereby quantifying the robustness of our results. revision: partial

  2. Referee: [Results (Fisher forecasts)] The handling of selection effects and Malmquist bias in the simulated high-z catalogs is not validated with redshift-split tests or explicit evolution corrections; without these, the claimed precision for a sample of ~66 optical GRBs may be optimistic and the comparison to Planck wCDM results cannot be taken at face value.

    Authors: The simulation procedure incorporates the observed distributions and selection effects from the real GRB population to construct the mock catalogs. However, we acknowledge that explicit validation through redshift-split tests was not presented. In the revised version, we have included additional tests splitting the observed sample into low- and high-redshift subsets to verify the consistency of the Dainotti relations and to assess potential biases. These tests support the validity of our approach, and we have updated the results section accordingly to include these validations, making the comparison to Planck more robust. revision: yes

  3. Referee: [§4 (cosmological parameter estimation)] The error propagation from the Dainotti relation parameters into the cosmological likelihood does not include marginalization over possible redshift evolution of the relation coefficients; this omission affects the standalone GRB constraints and their combination with CMB data.

    Authors: In our Fisher forecast methodology, the Dainotti relation parameters are fixed to their observed best-fit values, which is a common practice in such forecasting studies to provide baseline constraints. To address the referee's concern, we have revised §4 to include a marginalization over the uncertainties in the relation parameters, treating them as nuisance parameters. Additionally, we discuss the potential for redshift evolution and provide updated constraints that account for this. This strengthens the standalone GRB results and their combination with CMB data. revision: yes

Circularity Check

0 steps flagged

Forecasts are forward simulations using empirically fitted Dainotti relations; no reduction to self-definition or fitted inputs called predictions

full rationale

The paper fits the two-dimensional X-ray and optical Dainotti relations to the observed (mostly low-z) GRB population and uses those fixed parameters plus assumed scatter to generate simulated catalogs at z up to 9.2. Cosmological constraints on w (and w0, wa) are then obtained from these mocks via standard Fisher-matrix or likelihood methods. This chain does not reduce by construction to the input fits: the quoted precisions (e.g., σ_w ≈ 0.47 for ~66 optical GRBs) are explicit functions of sample size, redshift distribution, and relation scatter, not tautological re-statements of the fitted slope or normalization. Self-citation to prior Dainotti-relation papers is present but not load-bearing for the forecast procedure itself, which remains independent of the target cosmological parameters and externally falsifiable once real high-z GRBs are observed. No self-definitional, ansatz-smuggling, or renaming steps appear in the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The forecasts rest on the validity of the Dainotti relations at high redshift and the representativeness of simulated samples drawn from the observed GRB population; no new free parameters or invented entities are introduced beyond standard cosmological model assumptions.

axioms (1)
  • domain assumption The two-dimensional X-ray and optical Dainotti relations hold without significant evolution or selection bias for GRBs at redshifts up to z=9.2
    Invoked to justify using the relations for cosmological parameter constraints in the simulated high-z samples.

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Forward citations

Cited by 2 Pith papers

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  2. Magnetar-powered long gamma-ray bursts and connection to superluminous supernovae and fast radio bursts

    astro-ph.HE 2026-05 unverdicted novelty 5.0

    A sample of 169 magnetar-candidate long GRBs yields B_p proportional to P_0 to the power 0.83 and fields an order of magnitude stronger than those in superluminous supernovae.

Reference graph

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