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Spinor Field in Bianchi type-I Universe: regular solutions

Self-consistent solutions to the nonlinear spinor field equations in General Relativity has been studied for the case of Bianchi type-I (B-I) space-time. It has been shown that, for some special type of nonliearity the model provides regular solution, but this singularity-free solutions are attained at the cost of broken dominant energy condition in Hawking-Penrose theorem. It has also been shown that the introduction of $Λ$-term in the Lagrangian generates oscillations of the B-I model, which is not the case in absence of $Λ$ term. Moreover, for the linear spinor field, the $Λ$ term provides oscillatory solutions, those are regular everywhere, without violating dominant energy condition. Key words: Nonlinear spinor field (NLSF), Bianch type -I model (B-I), $Λ$ term PACS 98.80.C Cosmology