The Corrected Log N-Log Fluence Distribution of Cosmological Gamma-Ray Bursts

Recent analysis of relativistically expanding shells of cosmological gamma-ray bursts has shown that if the bursts are cosmological, then most likely total energy (E_0) is standard and not peak luminosity (L_0). Assuming a flat Friedmann cosmology (q_o = 1/2, Lambda = 0) and constant rate density (rho_0) 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 E_0 = 7.3^{+0.7}_{-1.0} X 10^{51} ergs and discuss implications of this energy for cosmological models of gamma-ray bursts.