Time dilation and the star formation scenario

We investigate the dependence of the redshift vs. brightness relation of GRBs upon the width of GRB luminosity function and the cosmological models. The relation is then fit to our observed time dilation data of GRBs. It is found that the best fit average luminosity ranges from L0 = 1.1 ± 0.3 1057 photons s-1 in a standard candle luminosity model to \u3c L \u3e = 8.7 ± 3.6 1057 photons s-1 in a cosmological model with a broad luminosity function φ(L) = C·L-β. Our fits suggest that it is only possible to accomodate the large distance scale suggested by the Star Formation Rate model when the luminosity function has a large width K ∼ 1000 in a cosmological model with low matter density Ω0