A Cosmology-independent Calibration of Gamma-ray Burst Luminosity Relations and the Hubble Diagram

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 lowredshift GRB sample. In this paper, we present a new method to calibrate GRB relations in a cosmologyindependent 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 ≤ 6.6, we obtain ΩM = 0.25+0.04 −0.05, ΩΛ = 0.75 +0.05 −0.04 for the flat ΛCDM model, and for the dark energy model with a constant equation of state w0 = −1.05+0.27 −0.40, which is consistent with the concordance model in a 1-σ confidence region. Subject headings: gamma rays: bursts — cosmology: observations