Cosmological extrapolation of modified Newtonian dynamics

The regime of modified Newtonian dynamics (MOND), which is used in astronomy to describe gravitating systems of the 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 the region under consideration. We show that such an 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 the evolving Universe, that are determined by the presence of a cosmological constant, the ordinary matter of baryons and electrons, and photon and neutrino radiation, without any dark matter. (paper)