Time Dilation in the Peak-to-Peak Time Scale of GRBs

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.