A cosmological independent calibration of the Ep,i-Eiso correlation for Gamma Ray Bursts

Abstract: The relation connecting the emitted isotropic energy and the rest-frame peak energy of the \nuF\nu spectra of Gamma-Ray Bursts (the Amati relation), strictly depends on the cosmological model, so we need a method to obtain an independent calibration of it. Using the Union Supernovae Ia catalog, we obtain a cosmographic luminosity distance in the y-redshift and demonstrate that this parametrization approximates very well the fiducial standard comsomlogical model \LambdaCDM. Furthermore, by this cosmographic luminosity distance dl, it is possible to achieve the Amati relation independent on the cosmological model. The cosmographic Amati relation that we obtain agrees, in the errors, with other cosmological-independent calibrations proposed in the literature. This could be considered a good indication in view to obtain standard candles by Gamma-Ray Bursts Key words. Gamma rays : bursts - Cosmology