Cosmological Time Dilation in Durations of Swift Long Gamma-Ray Bursts

Cosmological time dilation is a fundamental phenomenon in an expanding universe, which stresses that both the duration and wavelength of the emitted light from a distant object at the redshift z will be dilated by a factor of 1 + z at the observer. By using a sample of 139 Swift long gamma-ray bursts with known redshift (z <= 8.2), we measure the observed duration (T ₉₀) in the observed energy range between 140/(1 + z) keV and 350/(1 + z) keV, corresponding to a fixed energy range of 140-350 keV in the rest frame. We obtain a significant correlation between the duration and the factor 1 + z, i.e., T ₉₀ = 10.5(1 + z)^{0.94 ± 0.26}, which is consistent with that expected from the cosmological time dilation effect.