Calibration of GRB Luminosity Relations with Cosmography
  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. Finally, we constrain the dark energy parameterization models of the
Chevallier-Polarski-Linder (CPL) model, the Jassal-Bagla-Padmanabhan (JBP)
model and the Alam model with GRB data at high redshift, as well as with the
Cosmic Microwave Background radiation (CMB) and the baryonic acoustic
oscillation (BAO) observations, and we find the $\Lambda$CDM model is
consistent with the current data in 1-$\sigma$ confidence region.
