Autocorrelation functions ( ACFs ) are studied for a sample of 16 long gamma-ray bursts ( GRBs ) with known redshift z , that were observed by the BATSE and Konus experiments .
When corrected for cosmic time dilation , the ACF shows a bimodal distribution .
A narrow width class ( 11 bursts ) has at half-maximum a mean width \tau ^ { \prime } _ { o } = 1.6 s with a relative dispersion of \sim 32 % , while a broad width class ( 5 bursts ) has \tau ^ { \prime } _ { o } = 7.5 s with a \sim 4 % dispersion .
The separation between the two mean values is highly significant ( > 7 \sigma ) .
This temporal property could be used on the large existing database of GRBs with unknown redshift .
The broad width set shows a very good linear correlation between width at half-maximum and ( 1 + z ) , with a correlation coefficient R = 0.995 and a probability of chance alignment < 0.0004 .
The potential application of this correlation to cosmology studies is discussed , using it in combination with recently proposed luminosity indicators .