Long duration gamma-ray bursts may serve as standard candles to constrain cosmological parameters by probing the Hubble diagram well beyond the range of redshift currently accessible using SNe Ia. The standardization of gamma-ray bursts (GRBs) is based on phenomenological relations between two or more parameters found from spectral modeling, one of which is strongly dependent on the cosmological model. The Amati relation links the source-frame energy Ei,p at which the prompt gamma-ray spectral energy distribution νF ν peaks, and the isotropic-equivalent bolometric energy Eiso emitted during the prompt phase. We performed spectral analysis of 26 GRBs with known redshift that have been detected by the Fermi-Large Area Telescope (LAT) during its nine years of operations from 2008 July to 2017 September, thus extending the computation of E iso to the 100 MeV range. Multiple components are required to fit the spectra of a number of GRBs. We found that the Amati relation is satisfied by the 25 LGRBs, with best-fit parameters similar to previous studies that used data from different satellite experiments, while the only short GRB with known redshift 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 ΛCDM model, with Fermi-LAT GRBs alone and together with another sample of 94 GRBs and with the latest Supernovae type-Ia data. Our results are consistent with the currently acceptable ranges of those cosmological parameters within errors.
