Model-independent calibration of gamma-ray bursts with Bayesian neural networks
Abstract
Context. Gamma-ray bursts (GRBs) extend cosmological distance measurements beyond the range densely sampled by Type Ia supernovae, but their standardization requires reliable calibration and uncertainty estimates. Aims. We calibrate the Amati correlation without assuming a background cosmological model, assess its stability, and examine the cosmological reach of current and future GRB Hubble diagrams. Methods. We train a Bayesian neural network on Pantheon+ supernovae, assess and recalibrate its predictive uncertainties, and calibrate the correlation for GRBs at z ≤ 1.5 using the D'Agostini and Reichart likelihoods. We combine the GRB Hubble diagram with supernovae, Hubble-parameter measurements, and DESI baryon acoustic oscillations. Local-regression, covariance, leave-three-out, redshift-evolution, and Efron-Petrosian diagnostics test the standardization assumptions. We also analyse idealized future catalogues of 1500 standardized GRBs. Results. The diagram reaches z ≃ 9.4. Covariance and leave-three-out diagnostics produce small changes in the cosmological constraints. A parametric evolution coefficient is consistent with zero, whereas the truncation-corrected diagnostic indicates marginal isotropic-energy evolution that can occur along the Amati relation. Dark-energy extensions improve the phenomenological fit relative to flat ΛCDM: AIC favours the Chevallier-Polarski-Linder parametrization, while BIC favours constant-w dark energy. Forecasts show strong conditional model-discrimination power under the adopted uncertainty model. Conclusions. GRBs provide a complementary high-redshift extension of the supernova distance ladder. Present results do not establish an evolving dark-energy equation of state. Larger homogeneous samples are promising, but realistic selection functions and calibration systematics remain essential.
Related
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BibTeX
@misc{caterino2026modelindependent,
title = {{Model-independent calibration of gamma-ray bursts with Bayesian neural networks}},
author = {P. Caterino and M. Demianski and E. Piedipalumbo and L. Amati and D. De Cicco and M. Brescia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35503},
eprint = {2610.35503},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35503},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Model-independent calibration of gamma-ray bursts with Bayesian neural networks
AU - P. Caterino
AU - M. Demianski
AU - E. Piedipalumbo
AU - L. Amati
AU - D. De Cicco
AU - M. Brescia
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35503
UR - https://arxiv.org/abs/2610.35503
AB - Context. Gamma-ray bursts (GRBs) extend cosmological distance measurements beyond the range densely sampled by Type Ia supernovae, but their standardization requires reliable calibration and uncertainty estimates. Aims. We calibrate the Amati correlation without assuming a background cosmological model, assess its stability, and examine the cosmological reach of current and future GRB Hubble diagrams. Methods. We train a Bayesian neural network on Pantheon+ supernovae, assess and recalibrate its predictive uncertainties, and calibrate the correlation for GRBs at z ≤ 1.5 using the D'Agostini and Reichart likelihoods. We combine the GRB Hubble diagram with supernovae, Hubble-parameter measurements, and DESI baryon acoustic oscillations. Local-regression, covariance, leave-three-out, redshift-evolution, and Efron-Petrosian diagnostics test the standardization assumptions. We also analyse idealized future catalogues of 1500 standardized GRBs. Results. The diagram reaches z ≃ 9.4. Covariance and leave-three-out diagnostics produce small changes in the cosmological constraints. A parametric evolution coefficient is consistent with zero, whereas the truncation-corrected diagnostic indicates marginal isotropic-energy evolution that can occur along the Amati relation. Dark-energy extensions improve the phenomenological fit relative to flat ΛCDM: AIC favours the Chevallier-Polarski-Linder parametrization, while BIC favours constant-w dark energy. Forecasts show strong conditional model-discrimination power under the adopted uncertainty model. Conclusions. GRBs provide a complementary high-redshift extension of the supernova distance ladder. Present results do not establish an evolving dark-energy equation of state. Larger homogeneous samples are promising, but realistic selection functions and calibration systematics remain essential.
ER -