On the spectrum of Ultrahigh Energy Cosmic Rays and the Gamma Ray Burst   Origin Hypothesis
  It has been suggested that cosmological gamma-ray bursts (GRBs) can produce the observed flux of cosmic rays at the highest energies. However, recent studies of GRBs indicate that their redshift distribution likely follows that of the average star formation rate and that GRBs were more numerous at high redshifts. As a consequence, we show that photomeson production energy losses suffered by ultrahigh energy cosmic rays coming from GRBs would produce too sharp a spectral high energy cutoff to be consistent with the air shower data. Furthermore, we show that cosmological GRBs fail to supply the energy input required to account for the cosmic ray flux above 10 EeV by a factor of 100-1000. 
S.T. Scully and F.W. Stecker (NASA/GSFC)