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 (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(A) -> 0.9, Omega(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.