A Statistical Treatment of the Gamma-Ray Burst "No Host Galaxy" Problem:   II. Energies of Standard Candle Bursts
  With the discovery that the afterglows after some bursts are coincident with faint galaxies, the search for host galaxies is no longer a test of whether bursts are cosmological, but rather a test of particular cosmological models. The methodology we developed to investigate the original "no host galaxy" problem is equally valid for testing different cosmological models, and is applicable to the galaxies coincident with optical transients. We apply this methodology to a family of models where we vary the total energy of standard candle bursts. We find that total isotropic energies of E<2e52~erg are ruled out while log(E)~53 erg is favored. 
D. L. Band (UCSD), D. H. Hartmann (Clemson), and B. E. Schaefer (Yale)