Testing Dark Energy Models with Gamma-Ray Bursts Calibrated from the Observational $H(z)$ Data through a Gaussian Process

We use a cosmology-independent method to calibrate gamma-ray burst (GRB) from the observational Hubble data (OHD) with the cosmic chronometers method. By using Gaussian Process to reconstruct OHD, we calibrate the Amati relation ($E_{\rm p}$--$E_{\rm iso}$) to construct a GRB Hubble diagram with the A118 data set, and constrain Dark Energy models in a flat space with the Markov Chain Monte Carlo numerical method. With the cosmology-independent GRBs at $1.4<z\leq8.2$ in the A118 data set and the Pantheon sample of type Ia supernovae (SNe Ia) at $0.01<z\leq2.3$, we obtained $\Omega_{\rm m}$ = $0.379^{+0.033}_{-0.024}$, $h$ = $0.701^{+0.0035}_{-0.0035}$, $w$ = $-1.25^{+0.14}_{-0.12}$, $w_a$ = $-0.84^{+0.81}_{-0.38}$ for the flat Chevallier-Polarski-Linder model at the 1$\sigma$ confidence level. We find no significant evidence supporting deviations from the standard $\Lambda$CDM model.