Calibration of GRB Luminosity Relations with Cosmography

Understand

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.