Constraints on the Cosmological Parameters with Three-Parameter Correlation of Gamma-Ray Bursts

As one of the most energetic and brightest events, gamma-ray bursts (GRBs) can be treated as a promising probe high-redshift universe. Similar to type Ia supernovae (SNe Ia), GRBs with same physical origin could standard candles. We select GRB samples origin, which are divided into two groups. One group is consisted 31 plateau phase feature constant luminosity followed by decay index about -2 in X-ray afterglow light curves, other has 50 shallow optical curves. For selected samples, we confirm that there tight correlation between $L_0$, end time $t_b$ isotropic energy release $E_{\gamma,iso}$. also find $L_0-t_b-E_{\gamma,iso}$ insensitive cosmological parameters no valid limitations on obtained using this correlation. explore new three-parameter $t_b$, spectral peak rest frame $E_{p,i}$ ($L_0-t_b-E_{p,i}$), used candle constrain parameters. By employing sample only, constraints $\Omega_m = 0.697_{-0.278}^{+0.402}(1\sigma)$ for flat $\Lambda$CDM model. non-flat model, best-fitting results 0.713_{-0.278}^{+0.346}$, $\Omega_{\Lambda} 0.981_{-0.580}^{+0.379}(1\sigma)$. combination smaples, 0.313_{-0.125}^{+0.179}(1\sigma)$ 0.344_{-0.112}^{+0.176}$, 0.770_{-0.416}^{+0.366}(1\sigma)$