Constraints from Fermi observations of Long Gamma-Ray Bursts on cosmological parameters

In this paper, we compile a \emph{Fermi} sample of the \emph{long} GRB observations from 15 years of GBM catalogue with identified redshift, in which the GOLD sample contains 123 long GRBs at $z\le5.6$ and the FULL sample contains 151 long GRBs with redshifts at $z\le8.2$. The Amati relation (the $E_{\rm p,i}$-$E_{\rm iso}$ 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 $z\ge1.4$ 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 $z\ge1.4$ and the Pantheon+ sample of type Ia supernovae (SNe Ia) at $0.01<z\leq2.3$, we obtain $\Omega_{\rm m} = 0.354\pm0.018, H_0 = 73.05\pm0.2\,\rm{km/s/Mpc}$ for the flat $\Lambda$CDM model; $w_0 = -1.22^{+0.18}_{-0.15}$ for the flat $w$CDM model; and $w_{a} = -1.12^{+0.45}_{-0.83}$ 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.