Constraints from Fermi observations of long gamma-ray bursts on cosmological parameters

In this paper, we compile a Fermi sample of the long gamma-ray bursts (GRB) observations from 15 years of GBM catalogue with identified redshift, in which the GOLD sample contains 123 long GRBs at z <= 5.6 and the FULL sample contains 151 long GRBs with redshifts at z <= 8.2.The Amati relation (the E-p,E-i-E-iso correlation) are calibrated at z<1.4 by a Gaussian Process from the latest observational Hubble data (OHD) with the cosmic chronometers method so that GRBs at high-redshift z >= 1.4 can be used to constrain cosmological models via the Markov chain Monte Carlo (MCMC) method. From the cosmology-independent GRBs with the GOLD sample at z >= 1.4 and the Pantheon+ sample of type Ia supernovae (SNe Ia) at 0.01<z <= 2.3, we obtain Omega(m)=0.354 +/- 0.018,H-0=73.05 +/- 0.2km s(-1)Mpc(-1) for the flat Lambda CDM model; w(0)=-1.22(-0.15)(+0.18) for the flat wCDM model; and w(a)=-1.12(-0.83)(+0.45) for the flat Chevallier-Polarski-Linder model at the 1 sigma confidence level. Our results with the GOLD and FULL sample are almost identical, which are more stringent than the previous results with GRBs.