  The relation between the cosmological evolution of the jet-disk symbiosis
model for GRBs and the cosmic rays energy distribution is presented. We used
two different Star Formation Rates (SFR) as a function of redshift and a
Luminosity Function (LF) distribution to obtain the distribution in fluence of
GRBs in our model and compare it with the data. We show a good agreement
between the fluence distribution we obtain and the corrected data for the 4B
BATSE catalogue. The results we obtain are generally valid for models that use
jet physics to explain GRB properties. The fluence in the gamma ray band has
been used to calculate the energy in cosmic rays both in our Galaxy and at
extragalactic distances as a function of the redshift. This energy input has
been compared with the Galactic and extragalactic spectrum of cosmic rays and
neutrinos. Using our jet disk symbiosis model, we found that in both cases GRBs
cannot give any significant contribution to cosmic rays. We also estimate the
neutrino background, obtaining a very low predicted flux. We also show that the
fit of our model with the corrected fluence distribution of GRBs gives strong
constraints of the star formation rate as a function of the redshift.
