On the spectrum of ultrahigh energy cosmic rays and the γ-ray burst origin hypothesis

It has been suggested that cosmological γ-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 the average star formation rate of the universe 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 energy cutoff to be consistent with the air shower data. Futhermore, we show that cosmolgical GRBs fail to supply the energy input required to account for the cosmic ray flux above 1019 eV by a factor of 100–1000.