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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 approx 2.3 compared to the bright ones. With our canonical value of zmax = 2.1 the bright bursts originate at zbright approx 0.2. The corresponding expected ratio due to cosmological time dilation, 2.6, is in agreement with this measurement. Fenimore and Bloom [204] find, on the other hand, that when the fact that the burst's duration decreases as a function of energy as Deltat approx E-0.5 is included in the analysis, this time dilation corresponds to zmax > 6. This would require a strong negative intrinsic evolution: beta approx -1.5 ± 0.3. Alternatively, this might agree with the model in which the GRB rate follows the SFR [193, 195] which gives zmax approx 6. Cohen & Piran [191] suggested a way to perform the time dilation, spectral and red shift analysis simultaneously. Unfortunately current data are insufficient for this purpose.