Nonlinear Spinor Fields in Bianchi type-V spacetime

Abstract

A self-consistent system of nonlinear spinor and Bianchi type-V anisotropic gravitational fields are investigated. It is found that the presence of nontrivial non-diagonal components of the energy-momentum tensor of the spinor field imposes some severe restrictions to the system. As a result two different solutions are found. In one case the metric functions are similar to each other, i.e., $a_1 \sim a_2 \sim a_3$ and the spinor mass and spinor field nonlinearity do not disappear from the system. In this case the spacetime expands with acceleration in case of a positive self-coupling constant $\lambda$. A negative $\lambda$ gives rise to a cyclic or periodical mode of expansion. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly with time.