3.4. Time Dilation
Norris et al. [202, 203] examined 131 long bursts (with a duration longer than 1.5s) and found that the dimmest bursts are longer by a factor of 2.3 compared to the bright ones. With our canonical value of zmax = 2.1 the bright bursts originate at zbright 0.2. The corresponding expected ratio due to cosmological time dilation, 2.6, is in agreement with this measurement. Fenimore and Bloom  find, on the other hand, that when the fact that the burst's duration decreases as a function of energy as t E-0.5 is included in the analysis, this time dilation corresponds to zmax > 6. This would require a strong negative intrinsic evolution: -1.5 ± 0.3. Alternatively, this might agree with the model in which the GRB rate follows the SFR [193, 195] which gives zmax 6. Cohen & Piran  suggested a way to perform the time dilation, spectral and red shift analysis simultaneously. Unfortunately current data are insufficient for this purpose.