Nonlinear Spinor Fields in Bianchi type-I spacetime: Problems and Possibilities

TL;DR

This paper investigates the role of nonlinear spinor fields in Bianchi type-I cosmology, revealing how their non-diagonal energy-momentum tensor components impose restrictions that influence the universe's evolution and the nature of the equation of state.

Contribution

It provides a complete solution to the Einstein-spinor system under various restrictions, highlighting the conditions for non-trivial spinor fields and their impact on cosmological models.

Findings

Non-diagonal energy-momentum tensor components impose restrictions on spinor and metric functions.

Imposing restrictions on spinor fields leads to massless, trivial invariants.

Restricting metric functions yields FRW or LRS BI models with complete solutions.

Abstract

Within the scope of Bianchi type-I cosmological model we study the role of spinor field in the evolution of the Universe. It is found that due to the spinor affine connections the energy momentum tensor of the spinor becomes non-diagonal, whereas the Einstein tensor is diagonal. This non-triviality of non-diagonal components of the energy-momentum tensor imposes some severe restrictions either on the spinor field or on the metric functions or on both of them. In case if the restrictions are imposed on the components of spinor field only, we come to a situation when spinor field becomes massless and invariants constructed from bilinear spinor forms also become trivial. Imposing restriction wholly on metric functions we obtain FRW model, while if the restrictions are imposed both on metric functions and spinor field components, we come to LRS BI model. In both cases the system is solved completely. It was found that if the relation between the pressure and energy density obeys a barotropic equation of state, only a non-trivial spinor mass can give rise to a dynamic EoS parameter.