| An algorithm is designed to search for statistically significant peaks in the time profiles of Gamma Ray Bursts (GRBs) detected by the Burst And Transient Source Experiment (BATSE). Strong evidence of time dilation is found in the peak-to-peak time scales derived from GRBs with multiple peaks and duration greater than 2 seconds. The peak-to-peak time scales derived show that there is a factor of 1.92 ± 0.13 time stretching between bright and dim GRBs. The time stretching is interpreted as evidence of cosmological time dilation which stretches the light curves of GRBs by a factor of (1 + z). For the single peak bursts, their T90 duration distribution is found to be bimodal similar to all other bursts. The bimodality in the GRB distribution is not due to the distinction between bursts with a single peak and bursts with multiple peaks. The observed time dilation effect in the peak-to-peak time scales, together with the LogN–LogP number counts vs. brightness relation and direct redshift measurements of GRBs are used to constrain the luminosity function of GRBs for two cases of cosmological models. For the cosmological model with (Ω0, ΩΛ) = (10, 0.0), it is found that the time dilation relation and LogN–LogP relation calculated from the model are not compatible with the observational data. The cosmological model with (Ω0, ΩΛ ) = (0.3, 0.7) is found to reproduce all three pieces data if the density evolution of GRBs traces the star formation rate and the luminosity function has an average observable luminosity of ⟨Lobserved⟩ = 5.0 × 1051 ∼ 1.0 × 1052 ergs · s−1. This implies that majority of GRBs are at redshifts of 1∼3. |
