High Redshift Long Gamma-Ray Bursts Hubble Diagram as a Test of Basic Cosmological Relations

We examine the prospects of the high redshift Long Gamma Ray Bursts (LGRB) 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 LGRB 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 emphasise 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 $\Omega_\Lambda \rightarrow 0.9$, $\Omega_\text{m} \rightarrow 0.1$. Forthcoming gamma-ray observations by the space THESEUS mission together with ground and space based multimessenger facilities will allow us to improve essentially the restrictions on alternative basic principles of cosmological models.