Cosmological models of the Universe with reversal of the time arrow

Cosmological models of the Universe with reversal of the time arrow are considered. Formulations are presented of the hypotheses previously proposed by the author regarding cosmological CPT symmetry and also the multisheet open model with negative space curvature possibly involving the violation of CPT symmetry by an invariant combined charge. The statistical reversibility paradox is discussed for these models. The small dimentionless quantity σ2/α2 (α is the hyperbolic radius and σ-3 the entropy density), which characterizes the mean spatial curvature of the Universe, is explained as being the result of evolution of the Universe during numerous consecutive expansion-compession cycles