Nonlinear spinor fields in Bianchi type-I spacetime: problems and possibilities

Abstract

Recently many authors studied the Dirac spinors within the scope of different cosmological models with torsion [24-27, 37, 39]. Dirac spinors in Bianchi type-I f (R) cosmology with torsion was studied in [39], where it was shown that the dynamic behavior of the universe depends on the particular choice of the function f (R). In this paper tt was highlighted that, despite the anisotropic background the Einstein tensor is diagonal, whereas, because of intrinsic feature of spinor field, the energy tensor is non-diagonal. Dirac field equations coupled to electrodynamics and torsion fields were investigated in [27]. It was shown that minimal coupling between the torsion tensor and Dirac spinors generates a spin-spin interaction [25]. In [26] it was shown that the spacetime torsion, generated by Dirac spinors, induces gravitational repulsion. Nonsingular Dirac particles in spacetime with torsion were studied in [24].

Nonlinear spinor fields in Bianchi type-VI0 spacetime

“…It is found that in this case the non-diagonal components of the energy-momentum tensor of spinor field, unlike in the cases Bianchi type I [48] and Bianchi type-V I 0 [49], does not lead to the elimination of spinor field nonlinearity and the mass term in spinor field Lagrangian. Depending of the sign of self-coupling constant the model in this case allows either late time acceleration or oscillatory mode of evolution.…”

“…The existence of nontrivial non-diagonal components of the energy-momentum tensor plays a vital role in this matter. In [47,48] it was shown that depending on the type restriction imposed on the non-diagonal components of the energy-momentum tensor, the initially Bianchi type-I evolves into a LRS Bianchi type-I spacetime or FRW one from the very beginning, whereas the model may describe a general Bianchi type-I spacetime but in that case the spinor field becomes massless and linear. The same thing happens for a Bianchi type-V I 0 spacetime, i.e., the geometry of Bianchi type-V I 0 spacetime does not allow the existence of a massive and/or nonlinear spinor field [49].…”

Nonlinear spinor fields in Bianchi type-VI spacetime

“…The existence of nontrivial non-diagonal components of the energymomentum tensor plays a vital role in this matter. In [30,31] it was shown that depending on the type restriction imposed on the non-diagonal components of the energy-momentum tensor, the initially Bianchi type-I evolve into a LRS Bianchi type-I spacetime or FRW one from the very beginning, whereas the model may describe a general Bianchi type-I spacetime but in that case the spinor field becomes massless and linear. The same thing happens for a Bianchi type-V I 0 spacetime, i.e., the geometry of Bianchi type-V I 0 spacetime does not allow the existence of a massive and nonlinear spinor field in some particular cases [32].…”

Nonlinear Spinor Fields in Bianchi type-III Spacetime

“…In some recent studies [47][48][49] it was shown that due to its specific behavior in curve spacetime the spinor field can significantly change not only the geometry of spacetime but itself as well. The existence of nontrivial non-diagonal components of the energy-momentum tensor plays a vital role in this matter.…”

“…The existence of nontrivial non-diagonal components of the energy-momentum tensor plays a vital role in this matter. In [47,48] it was shown that depending on the type restriction imposed on the non-diagonal components of the energy-momentum tensor, the initially Bianchi type-I evolve into a LRS Bianchi type-I spacetime or FRW one from the very beginning, whereas the model may describe a general Bianchi type-I spacetime but in that case the spinor field becomes massless and linear. The same thing happens for a Bianchi type-V I 0 spacetime, i.e., the geometry of Bianchi type-V I 0 spacetime does not allow the existence of a massive and nonlinear spinor field in some particular cases [49].…”