**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
*z*_{max} = 2.1 the bright bursts originate at
*z*_{bright}
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
*t*
*E*^{-0.5} is included in the analysis,
this time dilation corresponds to *z*_{max} > 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 *z*_{max}
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.