Interacting self-consistent system of spinor and gravitational fields

Within the scope of simple cosmological models we have studied the role of spinor field in the evolution of the Universe when it is non-minimally coupled to the gravitational one. If the spinor field nonlinearity describes an ordinary matter such as radiation, the presence of non-minimality becomes essential and leads to the rapid expansion of the Universe in FRW model, but this is not the case for LRSBI model. If the spinor field nonlinearity describes a dark energy the role non-minimal coupling becomes insignificant in both isotropic and anisotropic models. © 2020 World Scientific Publishing Company.