A Cosmology Independent Calibration of GRB Luminosity Relations and the Hubble Diagram

An important issue related to the application of Gamma-Ray Bursts (GRBs) to cosmology is that the calibration of the luminosity relations of GRBs depends on the cosmological model due to the lack of sufficient low-redshift GRBs sample. In this paper, we present a new method to calibrate the GRB relations in a cosmological model independent way. Since sources at the same redshift should have the same luminosity distance, we obtain the distance modulus of a GRB at a given redshift by interpolating from the Hubble diagram of type Ia Supernovae (SNe Ia) of which the distance moduli are completely cosmological model independent. Then we calibrate seven GRB luminosity relations without assuming a particular cosmological model and construct the GRB Hubble diagram to constrain cosmological parameters. For a flat universe, we obtain ΩM = 0.25 +0.04 −0.05 and ΩΛ = 0.75 +0.05 −0.04 from 42 GRBs for 1.4 < z ≤ 6.6, which is consistent with the concordance model in 1-σ confidence region. Subject headings: gamma rays: bursts — cosmology: observations