Nonlinear spinor field in cosmology

Within the scope of the Bianchi type VI models, the self-consistent system of nonlinear spinor field and gravitational fields is considered. Exact self-consistent solutions to the spinor and gravitational field equations are obtained for a special choice of spatial inhomogeneity and nonlinear spinor term. The role of inhomogeneity in the evolution of spinor and gravitational field is studied. Some solutions allow an oscillating behavior of the Universe’s volume. It should be emphasized that for a suitable choice of spinor field nonlinearity some of these solutions are nonsingular at all space-time points.