If GRBs are at cosmological distances, there should be observational consequences:
-  Fainter bursts will, on average, be more distant.  
We would therefore expect them to show stronger cosmological time dilation effects --- 
the fainter bursts should have longer durations. 
This phenomenon has been observed.
 -  Similarly, fainter bursts will also be more redshifted, so the mean energy
of the photons in fainter bursts should be lower. 
This effect has also been observed. 
 
 
Of course, these effects could just reflect intrinsic differences 
between faint and bright GRBs...
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