Calibration of GRB Luminosity Relations with Cosmography

TL;DR

This paper introduces a cosmography-based method to calibrate GRB luminosity relations using SN Ia data, enabling high-redshift distance measurements and constraining dark energy models without assuming a specific cosmology.

Contribution

It proposes a novel calibration approach for GRB relations via cosmographic fitting directly from SN Ia data, improving high-redshift distance estimates.

Findings

Calibrated five GRB relations at z ≤ 1.4 using SN Ia data.

Deduced GRB distance moduli at 1.4 < z ≤ 6.6.

Found ΛCDM model consistent with current data within 1-σ confidence.

Abstract

For the use of Gamma-Ray Bursts (GRBs) to probe cosmology in a cosmology-independent way, a new method has been proposed to obtain luminosity distances of GRBs by interpolating directly from the Hubble diagram of SNe Ia, and then calibrating GRB relations at high redshift. In this paper, following the basic assumption in the interpolation method that objects at the same redshift should have the same luminosity distance, we propose another approach to calibrate GRB luminosity relations with cosmographic fitting directly from SN Ia data. In cosmography, there is a well-known fitting formula which can reflect the Hubble relation between luminosity distance and redshift with cosmographic parameters which can be fitted from observation data. Using the Cosmographic fitting results from the Union set of SNe Ia, we calibrate five GRB relations using GRB sample at $z\leq1.4$ and deduce distance moduli of GRBs at $1.4< z \leq 6.6$ by generalizing above calibrated relations at high redshift. Finally, we constrain the dark energy parameterization models of the Chevallier-Polarski-Linder (CPL) model, the Jassal-Bagla-Padmanabhan (JBP) model and the Alam model with GRB data at high redshift, as well as with the Cosmic Microwave Background radiation (CMB) and the baryonic acoustic oscillation (BAO) observations, and we find the $\Lambda$CDM model is consistent with the current data in 1-$\sigma$ confidence region.