One of the most intriguing features discovered by Swift is a plateau phase in the X-ray flux decay of about 70% of the afterglows of gamma-ray bursts (GRBs). The physical origin of this feature is still being debated. We constrain the proposed interpretations, based on the intrinsic temporal properties of the plateau phase. We selected and analyzed all the Swift/XRT GRB afterglows at known redshift observed between March 2005 and June 2008 featuring a shallow decay phase in their X-ray lightcurves. For our sample of 21 GRBs we find an anticorrelation of the logarithm of the duration of the shallow phase with re dshift, with a Spearman rank-order correlation coefficient of r=-0.4 and a null hypothesis probability of 5%. When we correct the durations for cosmological dilation, the anticorrelation strenghtens, with r=-0.6 and a null hypothesis probability of 0.4%. Considering only those GRBs in our sample that have a well-measured burst peak energy (8 out of 21), we find an anticorrelation between the energy of the burst and the shallow phase duration, with r=-0.80 and a null hypothesis probability of 1.8%. If the burst energy anticorrelation with the shallow phase duration is real, then the dependence of the shallow phase on redshift could be the result of a selection effect, since on average high-redshift bursts with lower energies and longer plateaus would be missed. A burst energy anticorrelation with the shallow phase duration would be expected if the end of the plateau arises from a collimated outflow. Alternative scenarios are briefly discussed involving a possible cosmological evolution of the mechanism responsible for the X-ray shallow decay.
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