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 \leq 6.6 , we obtain \Omega _ { 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 .