  The solution to the current extending Universe problem, and the description
of all stages of evolution compels scientists to consider various cosmological
models. Scalar - tensor models are rather simple and also allow us to clearly
define the separate stages of evolution. Furthermore, other cosmological models
are reduced. Our work takes into consideration the non-minimally interacted
scalar field and the spinor field. The spinor field has been considered to
establish a better understanding of the stages of evolution in our Universe.
