  With the Swift detection of GRB090423 at z = 8.2, it was confirmed that GRBs
are now detectable at (significantly) larger redshifts than AGN, and so can
indeed be used as probes of the Early Universe. The proposed Energetic X-ray
Imaging Survey Telescope (EXIST) mission has been designed to detect and
promptly measure redshifts and both soft X-ray (0.1 - 10 keV) and simultaneous
nUV-nIR (0.3 - 2.3microns) imaging and spectra for GRBs out to redshifts z ~18,
which encompasses (or even exceeds) current estimates for Pop III stars that
are expected to be massive and possibly GRB sources. Scaling from Swift for the
~10X greater sensitivity of EXIST, more than 100 GRBs at z >=8 may be detected
and would provide direct constraints on the formation and evolution of the
first stars and galaxies. For GRBs at redshifts z >= 8, with Lyman breaks at
greater than 1.12microns, spectra at resolution R = 30 or R = 3000 for
afterglows with AB magnitudes brighter than 24 or 20 (respectively) within
~3000sec of trigger will directly probe the Epoch of Reionization, formation of
galaxies, and cosmic star formation rate. The proposed EXIST mission can probe
these questions, and many others, given its unparalleled combination of
sensitivity and spatial-spectral-temporal coverage and resolution. Here we
provide an overview of the key science objectives for GRBs as probes of the
early Universe and of extreme physics, and the mission plan and technical
readiness to bring this to EXIST.
