Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae

In this paper, we calibrate the Amati relation (the $E_{\mathrm{p}}$-$E_{\mathrm{i}\mathrm{s}\mathrm{o}}$ correlation) of gamma-ray bursts (GRBs) in a cosmology-independent way. By using Gaussian process to reconstruct the smoothed luminosity distance from the Pantheon type Ia supernovae (SNe Ia) sample, we utilize the reconstructed results to calibrate the $E_{\mathrm{p}}$-$E_{\mathrm{i}\mathrm{s}\mathrm{o}}$ correlation with the Markov Chain Monte Carlo method and construct a Hubble diagram with the A220 GRB data, in which there are A118 GRB data with the higher qualities appropriate for cosmological purposes. With 98 GRBs at $1.4<z\le 8.2$ in the A118 sample and the observed Hubble data, we obtain ${\mathrm{\Omega }}_{\mathrm{m}}$=$0.346_{-0.069}^{+0.048}$, $h$=$0.677_{-0.029}^{+0.029}$ for the flat $\mathrm{\Lambda }$CDM model, and ${\mathrm{\Omega }}_{\mathrm{m}}$=$0.314_{-0.055}^{+0.072}$, $h$=$0.705_{-0.069}^{+0.055}$, $w$=$-1.23_{-0.64}^{+0.33}$ for the flat $w$CDM model, which are consistent with those from fitting the coefficients of the Amati relation and the cosmological parameters simultaneously.