We investigate the GeV emission from gamma-ray bursts (GRBs) using the results from the Energetic Gamma Ray Experimental Telescope (EGRET) and in view of the Gamma-Ray Large Area Space Telescope (GLAST). Assuming that the conventional prompt and afterglow photons originate from synchrotron radiation, we compare an accompanying inverse-Compton component with EGRET measurements and upper limits on GeV fluence, taking Klein-Nishina feedback into account. We find that the EGRET constraints are consistent with the theoretical framework of the synchrotron self-Compton model for both prompt and afterglow phases, and discuss constraints on microphysical parameters in both phases. Based on the inverse-Compton model and using EGRET results, we predict that GLAST would detect GRBs with GeV photons at a rate of ≥20 yr~(-1) from both the prompt and afterglow phases. This rate applies to the high-energy tail of the prompt synchrotron emission and to the inverse-Compton component of the afterglow. Theory predicts that in a large fraction of the cases where synchrotron GeV prompt emission would be detected by GLAST, inverse-Compton photons should also be detected at high energies (≥10 GeV). Therefore, GLAST will enable a more precise test of the high-energy emission mechanism. Finally, we show that the contribution of GRBs to the flux of the extragalactic gamma-ray background measured with EGRET is at least 0.01%, and likely around 0.1%.
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