Gamma-ray burst cosmology: Hubble diagram and star formation history
  We briefly introduce the disadvantages for Type Ia supernovae (SNe Ia) as
standard candles to measure the Universe, and suggest Gamma-ray bursts (GRBs)
can serve as a powerful tool for probing the properties of high redshift
Universe. We use GRBs as distance indicators in constructing the Hubble diagram
at redshifts beyond the current reach of SNe Ia observations. Since the
progenitors of long GRBs are confirmed to be massive stars, they are deemed as
an effective approach to study the cosmic star formation rate (SFR). A detailed
representation of how to measure high-$z$ SFR using GRBs is presented.
Moreover, first stars can form only in structures that are suitably dense,
which can be parameterized by defining the minimum dark matter halo mass
$M_{\rm min}$. $M_{\rm min}$ must play a crucial role in star formation. The
association of long GRBs with the collapses of massive stars also indicates
that the GRB data can be applied to constrain the minimum halo mass $M_{\rm
min}$ and to investigate star formation in dark matter halos.
