Spinor Field in Bianchi type-I Universe: regular solutions

TL;DR

This paper investigates regular solutions of nonlinear spinor fields in Bianchi type-I universes within General Relativity, highlighting the role of the cosmological constant in generating oscillatory and singularity-free models.

Contribution

It demonstrates that specific nonlinearities yield regular, singularity-free solutions that violate energy conditions, and shows the cosmological constant induces oscillations in these models.

Findings

Regular solutions exist for certain nonlinear spinor fields.

The $ ext{Lambda}$ term induces oscillations in B-I models.

Linear spinor fields with $ ext{Lambda}$ are regular and oscillatory.

Abstract

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 $\Lambda$-term in the Lagrangian generates oscillations of the B-I model, which is not the case in absence of $\Lambda$ term. Moreover, for the linear spinor field, the $\Lambda$ 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), $\Lambda$ term PACS 98.80.C Cosmology