Investigating signatures of cosmological time dilation in duration measures of prompt gamma-ray burst light curves

We study the evolution with redshift of three measures of gamma-ray burst (GRB) duration ($T_{\rm 90}$, $T_{\rm 50}$ and $T_{\rm R45}$) in a fixed rest frame energy band for a sample of 232 Swift/BAT detected GRBs. Binning the data in redshift we demonstrate a trend of increasing duration with increasing redshift that can be modelled with a power-law for all three measures. Comparing redshift defined subsets of rest-frame duration reveals that the observed distributions of these durations are broadly consistent with cosmological time dilation. To ascertain if this is an instrumental effect, a similar analysis of Fermi/GBM data for the 57 bursts detected by both instruments is conducted, but inconclusive due to small number statistics. We then investigate under-populated regions of the duration redshift parameter space. We propose that the lack of low-redshift, long duration GRBs is a physical effect due to the sample being volume limited at such redshifts. However, we also find that the high-redshift, short duration region of parameter space suffers from censorship as any Swift GRB sample is fundamentally defined by trigger criteria determined in the observer frame energy band of Swift/BAT. As a result, we find that the significance of any evidence for cosmological time dilation in our sample of duration measures typically reduces to $<2\sigma$.