Gamma-ray Burst Cosmology
  Gamma-ray bursts (GRBs) are the most luminous electromagnetic explosions in
the Universe, which emit up to $8.8\times10^{54}$ erg isotropic equivalent
energy in the hard X-ray band. The high luminosity makes them detectable out to
the largest distances yet explored in the Universe. GRBs, as bright beacons in
the deep Universe, would be the ideal tool to probe the properties of
high-redshift universe: including the cosmic expansion and dark energy, star
formation rate, the reionization epoch and the metal enrichment history of the
Universe. In this article, we review the luminosity correlations of GRBs, and
implications for constraining the cosmological parameters and dark energy.
Observations show that the progenitors of long GRBs are massive stars. So it is
expected that long GRBs are tracers of star formation rate. We also review the
high-redshift star formation rate derived from GRBs, and implications for the
cosmic reionization history. The afterglows of GRBs generally have broken
power-law spectra, so it is possible to extract intergalactic medium (IGM)
absorption features. We also present the capability of high-redshift GRBs to
probe the pre-galactic metal enrichment and the first stars.
