The Energetic X-ray Imaging Survey Telescope (EXIST) is designed to i) use the birth of stellar mass black holes, as revealed by cosmic Gamma-Ray Bursts (GRBs), as probes of the very first stars and galaxies to exist in the Universe. Both their extreme luminosity (~104 times larger than the most luminous quasars) and their hard X-ray detectability over the full sky with wide-field imaging make them ideal back-lights to measure cosmic structure with X-ray, optical and near-IR (nIR) spectra over many sight lines to high redshift. The full-sky imaging detection and rapid followup narrow-field imaging and spectroscopy allow two additional primary science objectives: ii) novel surveys of supermassive black holes (SMBHs) accreting as very luminous but rare quasars, which can trace the birth and growth of the first SMBHs as well as quiescent SMBHs (non-accreting) which reveal their presence by X-ray flares from the tidal disruption of passing field stars; and iii) a multiwavelength Time Domain Astrophysics (TDA) survey to measure the temporal variability and physics of a wide range of objects, from birth to death of stars and from the thermal to non-thermal Universe. These science objectives are achieved with the telescopes and mission as proposed for EXIST described here.
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