We present the Hubble diagram (HD) of 66 Gamma Ray Bursts (GRBs) derived using only data from their X - ray afterglow lightcurve. To this end, we use the recently updated L_X - T_a correlation between the break time T_a and the X - ray luminosity L_X measured at T_a calibrated from a sample of Swift GRBs with lightcurves well fitted by the Willingale et al. (2007) model. We then investigate the use of this HD to constrain cosmological parameters when used alone or in combination with other data showing that the use of GRBs leads to constraints in agreement with previous results in literature. We finally argue that a larger sample of high luminosity GRBs can provide a valuable information in the search for the correct cosmological model.
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