  In this paper, we demonstrate ASTRO-H's capability to measure the chemical
evolution in the high-z (z <~ 3) universe by observing X-ray afterglows of
gamma-ray bursts (GRBs) and distant Blazars. Utilizing these sources as
background light sources, the excellent energy resolution of ASTRO-H/SXS allows
us to detect emission and absorption features from heavy elements in the
circumstellar material in the host galaxies, from the intergalactic medium
(IGM) and in the ejecta of GRB explosions. In particular, we can constrain the
existence of the warm-hot intergalactic material (WHIM), thought to contain
most of the baryons at redshift of z < ~3, with a typical exposure of one day
for a follow-up observation of a GRB afterglow or 300 ks exposure for several
distant Blazars. In addition to the chemical evolution study, the combination
of the SGD, HXI, SXI and SXS will measure, for the first time, the temporal
behavior of the spectral continuum of GRB afterglows and Blazars over a broad
energy range and short time scales allowing detailed modeling of jets. The
ability to obtain these data from GRB afterglows will depend critically on the
availability of GRB triggers and the capability of ASTRO-H to respond rapidly
to targets of opportunity. At the present time it seems as if Swift will still
be functioning normally during the first two years of ASTRO-H operations
providing the needed triggering capability.
