Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae

TL;DR

This paper calibrates gamma-ray burst relations using Gaussian processes and Type Ia supernovae to construct a cosmology-independent Hubble diagram, providing constraints on cosmological parameters.

Contribution

It introduces a novel calibration method for GRB relations using Gaussian processes and SNe Ia, enabling cosmology-independent analysis.

Findings

Derived cosmological parameters consistent with previous studies.

Calibrated the Amati relation without assuming a cosmological model.

Constructed a Hubble diagram extending to high redshifts.

Abstract

In this paper, we calibrate the Amati relation (the $E_{\rm p}$-${E}_{\rm iso}$ correlation) of gamma-ray bursts (GRBs) in a cosmology-independent way. By using Gaussian process to reconstruct the smoothed luminosity distance from the Pantheon type Ia supernovae (SNe Ia) sample, we utilize the reconstructed results to calibrate the $E_{\rm p}$-${E}_{\rm iso}$ correlation with the Markov Chain Monte Carlo method and construct a Hubble diagram with the A220 GRB data, in which there are A118 GRB data with the higher qualities appropriate for cosmological purposes. With 98 GRBs at $1.4<z\leq8.2$ in the A118 sample and the observed Hubble data, we obtain $\Omega_{\rm m}$=$0.346^{+0.048}_{-0.069}$, $h$=$0.677^{+0.029}_{-0.029}$ for the flat $\Lambda$CDM model, and $\Omega_{\rm m}$=$0.314^{+0.072}_{-0.055}$, $h$=$0.705^{+0.055}_{-0.069}$, $w$=$-1.23^{+0.33}_{-0.64}$ for the flat $w$CDM model, which are consistent with those from fitting the coefficients of the Amati relation and the cosmological parameters simultaneously.