Spinor field in a Bianchi type-I universe: Regular solutions

Self-consistent solutions to the nonlinear spinor field equations in general relativity are studied for the case of Bianchi type-I (BI) space-time. It is shown that, for some special type of nonlinearity the model provides a regular solution, but this singularity-free solution is attained at the cost of breaking the dominant energy condition in the Hawking-Penrose theorem. It is also shown that the introduction of a $\Lambda$ term in the Lagrangian generates oscillations of the BI model, which is not the case in the absence of a $\Lambda$ term. Moreover, for the linear spinor field, the $\Lambda$ term provides oscillatory solutions, which are regular everywhere, without violating the dominant energy condition.