Modern Multimessenger Astronomy is a powerful instrument for performing crucial tests of the Standard
Cosmological Model in the wide redshift interval up to z ∼ 10. This testing 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 performed and planed
for THESEUS–BTA cooperative program. Such observations provide 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.