6.3.2. Dainotti or *L* <sup>X</sup>–*t*<sup>X</sup> Correlation

This correlation links the X-ray luminosity *L*<sup>X</sup> and rest-frame time *t*X, i.e., *L*<sup>X</sup> ∝ *t* −1 X , at the time when the X-ray afterglow light curve establishes a power-law decay after the plateau phase [136]. This correlation holds for LGRBs and SGRBEEs. By adding a third parameter, *E*iso, the new correlation of the form *L*<sup>X</sup> ∝ *t* −0.87 X *E* 0.88 iso [137] has been found. However, both relations are quite scattered and seem to be a selection effect due to the flux detection limit of *Swift*-XRT instrument. For details, see Ref. [130].

#### 6.3.3. *E* X iso–*E*iso–*E*<sup>p</sup> Correlation

This is a universal correlation for both LGRBs and SGRBs which links *E*iso and *E*<sup>p</sup> to the isotropic energy of the X-ray afterglow *E* X iso computed in the rest-frame energy band 0.3–

30 keV, i.e., *E* X iso ∝ *E* 1.00 iso *E* 0.60 p [138]. However, due to the fact that this correlation depends upon two cosmology-dependent quantities, it is unsuitable to constrain cosmological parameters. For details, see Ref. [139].
