Recent analysis of relativistically expanding shells of cosmological γ-ray bursts has shown that if the bursts are cosmological, then most likely total energy (E0) is standard and not peak luminosity (L0). Assuming a flat Friedmann cosmology (q0=1/2, λ=0) and constant rate density (ρ0) of bursting sources, we fit a standard candle energy to a uniformly selected log N-log S in the BATSE 3B catalog correcting for fluence efficiency and averaging over 48 observed spectral shapes. We find the data consistent with E0=7.3−1.0+0.7×1051 ergs and discuss implications of this energy for cosmological models of γ-ray bursts.
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Bloom et al. (1996) studied this question.