We examine the prospects of the high-redshift long gamma-ray bursts (LGRBs) Hubble diagram as a test of the basic cosmological principles. Analysis of the Hubble diagram allows us to test several fundamental cosmological principles using the directly observed flux–distance–redshift relation. Modern LGRBs data together with the correlation between the spectral peak energy and the isotropic equivalent radiated energy (the so-called Amati relation) can be used for construction of the Hubble diagram at the model-independent level. We emphasize observational selection effects, which inevitably exist and distort the theoretically predicted relations. An example is the weak and strong gravitational lensing bias effect for high-redshift LGRB in the presence of limited observational sensitivity (Malmquist bias). After bias correction, there is a tendency to vacuum-dominated models with |$\Omega _\Lambda \rightarrow 0.9$|⁠, Ω_m → 0.1. Forthcoming gamma-ray observations by the Transient High-Energy Sky and Early Universe Surveyor (THESEUS) space mission together with ground- and space-based multimessenger facilities will allow us to improve essentially the restrictions on alternative basic principles of cosmological models.

中文翻译：

---

高红移长伽马射线爆发哈勃图作为基本宇宙关系的测试

我们研究了高红移长伽马射线暴 (LGRB) 哈勃图的前景，作为对基本宇宙学原理的测试。对哈勃图的分析使我们能够使用直接观察到的通量-距离-红移关系来测试几个基本的宇宙学原理。现代 LGRBs 数据以及光谱峰值能量与各向同性等效辐射能量之间的相关性（所谓的 Amati 关系）可用于构建与模型无关的哈勃图。我们强调观察选择效应，它不可避免地存在并扭曲了理论预测的关系。一个例子是在观测灵敏度有限的情况下（马尔奎斯特偏差），高红移 LGRB 的弱引力透镜偏差效应和强引力透镜偏差效应。偏差修正后，有|$\Omega _\Lambda \rightarrow 0.9$|⁠，Ω_m → 0.1 的真空支配模型的趋势。瞬态高能天空和早期宇宙勘测者 (THESEUS) 太空任务即将进行的伽马射线观测以及地面和太空多信使设施将使我们能够从根本上改善对宇宙学模型替代基本原理的限制。