On certain properties of cosmological models

Abstract. It is shown that in homogeneous cosmological models the Einstein equations can be reduced, on the basis of scale invariance, to systems with fric-tion. The formalism involving friction permits one to investigate the problem of isotropization of the solutions in the Bianchi model IX at late development stages. The possibility of a statistical description of the properties of the model is discussed. A number of investigations of the last decade have been devoted to the question (first explicitly formulated by Landau) of the singularities of the solutions of Ein-stein’s equations in cosmological models more general than the classical Friedmann model. Special mention should be made (in addition to the ideologically useful but ineffective theorems of Penrose et al.) of the papers by Belinskii, Lifshitz, and Khalatnikov (BLKh)[4], devoted, in particular, to the asymptotic solution of the so-called Bianchi model IX (and also VIII), which they were the first to investigate, when the singularity is approached. This asymptotic behavior turned out to be quite interesting. Recently, the question of the properties of this model near th