Spinor field in cosmology with Lyra’s geometry: Bianchi type-I model

Within the scope of a Bianchi type-I cosmological model with Lyra’s geometry we study the role of a nonlinear spinor field in the evolution of Universe. Earlier we have considered the nonlinear spinor field in different anisotropic and isotropic cosmological models and it was found that the presence of nontrivial non-diagonal components of energy-momentum tensor of spinor field leads to some severe restrictions on both space-time geometry and spinor field. In this study we have found that though the restrictions remain in place, the introduction of Lyra's geometry plays significant role in the evolution of Universe due to the fact that invariants of spinor field depends on the parameter of Lyra's geometry.