2023ApJ...953...58L

As one of the most energetic and brightest events, gamma-ray bursts (GRBs) can be treated as a promising probe of the high-redshift universe. Similar to type Ia supernovae, GRBs with the same physical origin could be treated as standard candles. We select GRB samples with the same physical origin, which are divided into two groups. The first group consists of 31 GRBs with a plateau phase feature of a constant luminosity followed by a decay index of about -2 in the X-ray afterglow light curves, and the second group has 50 GRBs with a shallow decay phase in the optical light curves. For the selected GRB samples, we confirm that there is a tight correlation between the plateau luminosity L₀, the end time of plateau t_b, and the isotropic energy release E_γ,iso. We also find that the L₀-t_b - E_γ,iso correlation is insensitive to the cosmological parameters and that no valid limitations on the cosmological parameters can be obtained using this correlation. We explore a new three-parameter correlation L₀, t_b, and the spectral peak energy in the rest-frame E_p,i (L₀-t_b-E_p,i), and find that this correlation can be used as a standard candle to constrain the cosmological parameters. By employing the optical sample only, we find the constraints of ${{\rm{\Omega }}}_{m}={0.697}_{-0.278}^{+0.402}(1\sigma )$ for a flat ΛCDM model. For the non-flat ΛCDM model, the best-fitting results are ${{\rm{\Omega }}}_{m}={0.713}_{-0.278}^{+0.346}$, ${{\rm{\Omega }}}_{{\rm{\Lambda }}}={0.981}_{-0.580}^{+0.379}(1\sigma )$. For the combination of the X-ray and optical samples, we find ${{\rm{\Omega }}}_{m}={0.313}_{-0.125}^{+0.179}(1\sigma )$ for a flat ΛCDM model, and ${{\rm{\Omega }}}_{m}={0.344}_{-0.112}^{+0.176}$, ${{\rm{\Omega }}}_{{\rm{\Lambda }}}={0.770}_{-0.416}^{+0.366}(1\sigma )$ for a non-flat ΛCDM model.