(Feraol Dirirsa and Fred Piron on behalf of the Fermi-LAT Collaboration)
Long duration Gamma-Ray Bursts (LGRBs) may serve as standard candles to constrain cosmological parameters by probing the Hubble diagram well beyond the range of redshift currently accessible using type-Ia supernovae. The standardization of LGRBs is based on phenomenological relations between two or more parameters found from spectral modeling, of which one is strongly dependent on the cosmological model. The Amati relation is between the source-frame energy Ei,p at which the prompt gamma-ray spectral energy distribution nu F_nu peaks, and the isotropic-equivalent bolometric energy Eiso emitted during the prompt phase. We perform spectral analysis of 26 GRBs with known redshift that are detected by the Fermi-Large Area Telescope (LAT) during its nine years of operations from July 2008 to September 2017, thus extending the computation of Eiso to the 100 MeV range. Multiple components are required to fit the spectra of a number of GRBs. We find that the Amati relation is satisfied by the 25 LGRBs, with fitting parameters similar to previous studies that used data from different satellite experiments, while the sole short GRB is an outlier. Using the Amati relation we extend the Hubble diagram to redshift 4.35 and constrain the Hubble constant and dark-energy density in the Lambda-CDM model, with Fermi-LAT GRBs alone and together with another GRB sample and with the latest SNe-Ia data. Our results are consistent with the currently acceptable ranges of those cosmological parameters.