Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8221Research ArticleSpinor Model of the Transition of the Universe from the Slow Expansion to the Accelerating OneKovalchukovN ADepartment of Theoretical Physics and Mechanicsn.kovalchukov@rudn.ruShikinG NDepartment of Theoretical Physics and Mechanics-YuschenkoL PDepartment of Theoretical Physics and Mechanicsyuschenko_leonid@mail.ruPeoples’ Friendship University of Russia150420154566008092016Copyright © 2015,2015According to the astronomical data our Universe is expanding with acceleration in the present stage. One of the possible explanation of such evolution is that in the present epoch about 70% of the total mass of the Universe is represented by dark energy(cosmic vacuum). Under simulating of the matter of the Universe we use the state equation of the form P =Wɛ, where P is pressure, ɛ is energy density. Under such state equation W = -1 corresponds to dark energy, that leads us to the state equation of the ideal ﬂuid with negative pressure: P= -ɛ 0. This case corresponds to the cosmological constant. The transition from the slow expansion to the accelerating one means that at some stage of the evolution acceleration a(t) changes it’s sign from minus to plus. In this case the parameter W changes from values W -1 to the value W = -1. It is notable that the case - 1 W -1 3 corresponds to the quintessence, and W -1 - to the phantom matter. In this work we consider the transition of the Universe from the slow expansion to the accelerating one on the assumption that the Universe is ﬁlled by spinor matter.spinor matteraccelerationdark energyideal fluidquintessencephantom matterспинорная материяускорениетёмная энергияидеальная жидкостьквинтэссенцияфантомная материя