Constraints on Cosmological Models and Reconstructing the Acceleration
  History of the Universe with Gamma-Ray Burst Distance Indicators
  Gamma-ray bursts (GRBs) have been regarded as standard candles at very high
redshift for cosmology research. We have proposed a new method to calibrate GRB
distance indicators with Type Ia supernova (SNe Ia) data in a completely
cosmology-independent way to avoid the circularity problem that had limited the
direct use of GRBs to probe cosmology [N. Liang, W. K. Xiao, Y. Liu, and S. N.
Zhang, Astrophys. J. 685, 354 (2008).]. In this paper, a simple method is
provided to combine GRB data into the joint observational data analysis to
constrain cosmological models; in this method those SNe Ia data points used for
calibrating the GRB data are not used to avoid any correlation between them. We
find that the $\Lambda$CDM model is consistent with the joint data in the
1-$\sigma$ confidence region, using the GRB data at high redshift calibrated
with the interpolating method, the Constitution set of SNe Ia, the cosmic
microwave background radiation from Wilkinson Microwave Anisotropy Probe five
year observation, the baryonic acoustic oscillation from the spectroscopic
Sloan Digital Sky Survey Data Release 7 galaxy sample, the x-ray baryon mass
fraction in clusters of galaxies, and the observational Hubble parameter versus
redshift data. Comparing to the joint constraints with GRBs and without GRBs,
we find that the contribution of GRBs to the joint cosmological constraints is
a slight shift in the confidence regions of cosmological parameters to better
enclose the $\Lambda$CDM model. Finally, we reconstruct the acceleration
history of the Universe up to $z>6$ with the distance moduli of SNe Ia and GRBs
and find some features that deviate from the $\Lambda$CDM model and seem to
favor oscillatory cosmology models; however further investigations are needed
to better understand the situation.
