Gamma-ray bursts (GRBs), as a possible probe to extend the Hubble diagram to high redshifts, have attracted much attention recently. In this paper, we select two samples of GRBs that have a plateau phase in X-ray afterglow. One is short GRBs (SGRBs) with plateau phases dominated by magnetic dipole (MD) radiations. The other is long GRBs (LGRBs) with gravitational wave (GW) dominated plateau phases. These GRBs can be well standardized using the correlation between the plateau luminosity L0 and the end time of plateau tb. The so-called circularity problem is mitigated by using the observational Hubble parameter data and Gaussian process method. The calibrated L0 – tb correlations are also used to constrain Lambda cold dark matter (ΛCDM) and w(z) = w0 models. Combining the MD–LGRBs sample from Wang et al. (2021) and the MD–SGRBs sample, we find $\Omega _{\mathrm{ m}} = 0.33_{-0.09}^{+0.06}$ and ΩΛ = $1.06_{-0.34}^{+0.15}$ excluding systematic uncertainties in the non-flat ΛCDM model. Adding Type Ia supernovae from Pantheon sample, the best-fitting results are w0 = $-1.11_{-0.15}^{+0.11}$ and Ωm = $0.34_{-0.04}^{+0.05}$ in the w = w0 model. These results are in agreement with the ΛCDM model. Our result supports that selection of GRBs from the same physical mechanism is crucial for cosmological purposes.

中文翻译：

---

用伽马射线爆发的光度-时间相关性测量宇宙学参数

伽马射线暴（GRB）作为将哈勃图扩展到高红移的一种可能的探测器，最近引起了广泛关注。在本文中，我们选择了两个在 X 射线余辉中具有平台阶段的 GRB 样本。一种是短伽马暴（SGRBs），其平台相以磁偶极子（MD）辐射为主。另一种是长伽马暴（LGRBs），以引力波（GW）为主的高原阶段。利用高原光度 L0 和高原结束时间 tb 之间的相关性，这些 GRB 可以很好地标准化。通过使用观测的哈勃参数数据和高斯过程方法来缓解所谓的圆度问题。校准后的 L0 – tb 相关性也用于约束 Lambda 冷暗物质 (ΛCDM) 和 w(z) = w0 模型。结合 Wang 等人的 MD-LGRBs 样本。(2021) 和 MD-短暴样本，我们发现 $\Omega _{\mathrm{ m}} = 0.33_{-0.09}^{+0.06}$ 和 ΩΛ = $1.06_{-0.34}^{+0.15}$ 不包括非平坦 ΛCDM 中的系统不确定性模型。加入 Pantheon 样本中的 Ia 型超新星，最佳拟合结果为 w0 = $-1.11_{-0.15}^{+0.11}$ 和 Ωm = $0.34_{-0.04}^{+0.05}$ 在 w = w0模型。这些结果与ΛCDM模型一致。我们的结果支持从相同物理机制中选择 GRB 对于宇宙学目的至关重要。