Fourier analysis of gamma-ray burst light curves: Searching for a direct signature of cosmological time dilation

We study the power density spectrum (PDS) of light curves of the observed gamma-ray bursts (GRBs) to search for a direct signature for cosmological time dilation in the PDS statistics with the GRBs whose redshifts z are known. The anticorrelation of a timescale measure and a brightness measure is indirect evidence of its effect. On the other hand, we directly demonstrate that a time dilation effect can be seen in GRB light curves. We find that timescales tend to be shorter in bursts with small redshift, as expected from cosmological time dilation effects, and we also find that there may be noncosmological effects contributing to this correlation. We discuss the implications of this result on interpretations of the PDS analysis results. We put forward another caution regarding this kind of analysis when we statistically work with GRBs whose z is unknown.