3 Conclusion

The uncertainties in the GRB luminosity function and cosmological parameters can easily translate into an order of magnitude uncertainty in using the time dilation or directly measured redshift vs. peak flux relation to constrain the distance scale and luminosity of GRBs. These should be taken into account when one attempts to distinguish between the traditional models with $z \sim 1$ and the SFR models with GRBs at much higher redshifts $z \sim 5-6$ (Wijers [1997]) for dim GRBs with peak flux $P\sim 0.3 \ {\rm photons} \ {\rm s}^{-1}\ {\rm cm}^{-2}$. For SFR models which require a peak luminosity $L \sim 10^{58}\ {\rm photons} \ {\rm s}^{-1}$, the above fits suggest that it is only possible to accomodate such a scenario when the luminosity function has a large width $K \sim 1000$ in a cosmological model with low matter density $\Omega_{0} = 0.3$.