THESEUS$-$BTA cosmological tests using Multimessenger Gamma-Ray Bursts observations

Modern Multimessenger Astronomy opens unique possibility for performing cosmological tests of the Standard Cosmological Model in the wide redshift interval up to $z \sim 10$. This is principally important for recent discussion related to discrepancies between local and global measurements of cosmological parameters. We present a review of multimessenger Gamma-Ray Bursts observations currently performed and planed for THESEUS-BTA cooperative program. Such observations allow testing the fundamental basis of cosmological models: gravitation theory; cosmological principle of homogeneity and isotropy of the large scale matter distribution; and space expansion paradigm. Important role of different selection effects, which lead to systematic distortions of the true cosmological relations, is discussed.