Constraining cosmological parameters by gamma-ray burst X-ray afterglow light curves

We present the Hubble diagram (HD) of 66 gamma-ray bursts (GRBs) derived using only data from their X-ray afterglow light curve. 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 light curves well fitted by the Willingale et al. 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.