We present strong evidence of time stretching in the peak-to-peak time scales in the light curves of BATSE Gamma Ray Bursts ( GRBs ) .
Extensive tests are performed on artificially dilated bursts to verify that the procedure for extracting the peak-to-peak time scales correctly recovers the stretching of bursts .
The resulting robust algorithm is then applied to the 4B GRB database .
We derive a stretching factor of 1.92 \pm 0.13 between the brightest burst group ( P > 7.7 photon \cdot cm ^ { -2 } \cdot s ^ { -1 } ) and the dimmest burst group ( P = 1.0 \sim 1.4 photon \cdot cm ^ { -2 } \cdot s ^ { -1 } ) with several independent peak-to-peak time scale definitions and they agree within uncertainties .
Such an agreement strongly supports the interpretation of the observed time stretching as time dilation caused by the cosmological expansion , rather than physical selection effects .
We fit the result to cosmological models with \Lambda = 0 , \Omega _ { 0 } from 0.2 to 1.0 , and contrained the standard candle luminosity to be L _ { 0 } = 7.0 \pm 2.0 \pm 2.7 \times 10 ^ { 56 } photons \cdot s ^ { -1 } .
Our luminosity value is fully consistent with the value from the combined PVO and BATSE LogN-LogP curve with the BATSE bright bursts at low redshifts of z _ { bright } = 0.11 \pm 0.02 \pm 0.025 .
This luminosity fit is definitely inconsistent with the the larger distance scale implied from associating burst density with star formation rates .