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 p
resent 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 $1.4<zle6.6$, 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.
This report is an update and extension of our paper accepted for publication in ApJ (arXiv:0802.4262). Since objects at the same redshift should have the same luminosity distance and the distance moduli of type Ia supernovae (SNe Ia) obtained directl
y from observations are completely cosmology independent, we obtain the distance modulus of a gamma-ray burst (GRB) at a given redshift by interpolating or iterating from the Hubble diagram of SNe Ia. Then we calibrate five GRB relations without assuming a particular cosmological model, from different regression methods, and construct the GRB Hubble diagram to constrain cosmological parameters. Based upon these relations we list the cosmology-independent distance moduli of 42 GRBs between redshift of 1.44 and 6.60, with the 1-$sigma$ uncertainties of 1-3%.
