Tightening Cosmological Constraints Within and Beyond $\Lambda$CDM Using Gamma-Ray Bursts Calibrated with Type Ia Supernovae

TL;DR

This paper develops a model-independent method to calibrate gamma-ray bursts as high-redshift distance indicators, combining neural network reconstructions with supernova data to improve cosmological constraints beyond the standard model.

Contribution

It introduces a novel, self-consistent calibration technique for GRBs using neural networks and supernova data, extending the cosmic distance ladder to higher redshifts.

Findings

Consistent cosmological constraints from two GRB correlations.

Hubble constant aligns with supernova measurements.

High-redshift GRBs suggest higher matter density and potential dark energy evolution.

Abstract

Context. Gamma-ray bursts (GRBs) reach redshifts beyond Type Ia supernovae (SNe Ia) and can extend distance measurements into the early Universe, but their use as distance indicators is limited by the circularity problem in calibrating empirical luminosity relations. Aims. We present a model-independent methodology to overcome this circularity by combining Pantheon$+$ SNe Ia, a distance reconstruction based on artificial neural networks (ANNs), and two GRB correlations (Amati and Combo) into a distance ladder from low to high redshift, with the goal of constraining cosmological parameters in $\Lambda \mathrm{CDM}$ and $w_0 w_a \mathrm{CDM}$. Methods. We use the ReFANN to reconstruct the luminosity distance $d_L(z)$ and distance modulus $\mu(z)$ from the Pantheon$+$ dataset, with hyperparameters optimized via approximate Bayesian computation rejection and a risk function. This model-independent reconstruction calibrates the Amati and Combo relations using a low-redshift ($z<1$) GRB sample from Fermi GBM and Swift-XRT. The calibrated relations then provide distance estimates for GRBs at $z \geq 1$. Finally, a joint Bayesian analysis simultaneously constrains the cosmological and GRB correlation parameters, ensuring self-consistent uncertainty propagation. Results. We obtain consistent cosmological constraints from two independent GRB correlations. The Hubble constant $H_0$ agrees with SNe Ia values, though potentially influenced by Pantheon$+$ dataset. High-redshift GRBs favour a higher matter density $\Omega_m$ than the Pantheon$+$ and hint at possible dark energy evolution.Conclusions. We present a framework that mitigates GRB cosmology's circularity problem, extending the distance ladder to $z \sim 9$ and establishing GRBs as a high-redshift probe.