Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way

In this paper, we present a cosmology-independent method to constrain cosmological models from the latest 221 gamma-ray bursts (GRBs) sample, including 49 GRBs from Fermi catalog with the Amati relation (the $E_{\mathrm{p}}$-$E_{\mathrm{i}\mathrm{s}\mathrm{o}}$ correlation), which are calibrated by using a Gaussian process from the Pantheon+ type Ia supernovae (SNe Ia) sample. With 182 GRBs at $0.8\le z\le 8.2$ in the Hubble diagram and the latest observational Hubble data (OHD) by the Markov Chain Monte Carlo (MCMC) method, we obtained ${\mathrm{\Omega }}_{\mathrm{m}}$ = $0.348_{-0.066}^{+0.048}$ and $h$ = $0.680_{-0.029}^{+0.029}$ for the flat $\mathrm{\Lambda }$CDM model, and ${\mathrm{\Omega }}_{\mathrm{m}}$ = $0.318_{-0.059}^{+0.067}$, $h$ = $0.704_{-0.068}^{+0.055}$, $w$ = $-1.21_{-0.67}^{+0.32}$ for the flat $w$CDM model. These results are consistent with those in which the coefficients of the Amati relation and the cosmological parameters fitted simultaneously.