A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram

TL;DR

This paper introduces a new cosmology-independent method to calibrate gamma-ray burst relations using Type Ia supernova data, enabling more reliable use of GRBs for cosmological measurements without assuming a specific cosmological model.

Contribution

The authors develop a novel calibration technique for GRB luminosity relations that does not depend on any cosmological assumptions, improving the use of GRBs as standard candles.

Findings

Calibrated seven GRB relations without assuming a cosmological model.

Constructed a GRB Hubble diagram to constrain cosmological parameters.

Results are consistent with the standard cosmological model within 1-sigma confidence.

Abstract

An important concern in the application of gamma-ray bursts (GRBs) to cosmology is that the calibration of GRB luminosity/energy relations depends on the cosmological model, due to the lack of a sufficient low-redshift GRB sample. In this paper, we present a new method to calibrate GRB relations in a cosmology-independent way. Since objects at the same redshift should have the same luminosity distance and since the distance moduli of Type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a GRB at a given redshift by interpolating from the Hubble diagram of SNe Ia. Then we calibrate seven GRB relations without assuming a particular cosmological model and construct a GRB Hubble diagram to constrain cosmological parameters. From the 42 GRBs at $1.4<z\le6.6$, we obtain $\Omega_{\rm M}=0.25_{-0.05}^{+0.04}$, $\Omega_{\Lambda}=0.75_{-0.04}^{+0.05}$ for the flat $\Lambda$CDM model, and for the dark energy model with a constant equation of state $w_0=-1.05_{-0.40}^{+0.27}$, which is consistent with the concordance model in a 1-$\sigma$ confidence region.