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.
