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

Modern Multimessenger Astronomy is a powerful instrument for performing cosmological crucial tests of the Standard Cosmological Model in the wide redshift interval up to $z\sim 10$. This is principally important for discussion related to discrepancies between local and global measurements of cosmological parameters. We present a review of multimessenger gamma-ray burst observations currently conducted and planed for THESEUS$-$BTA cooperative program. Such observations give a unique opportunity to test the fundamental foundations of cosmological models: gravitation theory; cosmological principle of homogeneity and isotropy of large-scale distribution of matter; and space expansion paradigm. Important role of various selection effects leading to systematic distortions of true cosmological relations is discussed.