Spinor field in Bianchi type-$IX$ space-time

Abstract

Within the scope of Bianchi type-$IX$ we have studied the role of spinor field in the evolution of the Universe. It is found that unlike the diagonal Bianchi models in this case the components of energy-momentum tensor of spinor field along the principal axis are not the same, i.e. $T_1^1\ne T_2^2\ne T_3^3$, even in absence of spinor field nonlinearity. The presence of nontrivial non-diagonal components of energy-momentum tensor of the spinor field imposes severe restrictions both on geometry of space-time and on the spinor field itself. As a result the space-time turns out to be either locally rotationally symmetric or isotropic. In this paper we considered the Bianchi type-$IX$ space-time both for a trivial $b$, that corresponds to standard $BIX$ and the one with a non-trivial $b$. It was found that a positive ${\lambda }_1$ gives rise to an oscillatory mode of expansion, while a trivial ${\lambda }_1$ leads to rapid expansion at the early stage of evolution.

20 pages, 12 Figures, in the previous version there were some mistakes which are corrected, beside the conventional Bianchi type IX model a model with a more general $h(x_3)$ is studied

References in corpus (3)

• Zero Energy of Plane-Waves for ELKOs
• Nonlinear Spinor Fields in Bianchi type-VI spacetime
• Nonlinear Spinor Fields in Bianchi type-III spacetime