Cosmological extrapolation of MOND

Regime of MOND, which is used in astronomy to describe the gravitating systems of island type without the need to postulate the existence of a hypothetical dark matter, is generalized to the case of homogeneous distribution of usual matter by introducing a linear dependence of the critical acceleration on the size of region under consideration. We show that such the extrapolation of MOND in cosmology is consistent with both the observed dependence of brightness on the redshift for type Ia supernovae and the parameters of large-scale structure of Universe in the evolution, that is determined by the presence of a cosmological constant, the ordinary matter of baryons and electrons as well as the photon and neutrino radiation without any dark matter.