Eur. Phys. J. Plus (2017) 132: 547
https://doi.org/10.1140/epjp/i2017-11830-0

Regular Article

Bianchi type-VIII spinor solutions

Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia

^* e-mail: bijan@jinr.ru

Received: 12 July 2017
Accepted: 5 December 2017
Published online: 28 December 2017

Abstract

Within the scope of Bianchi type-VIII space-time the role of nonlinear spinor field in the evolution of the Universe is studied. 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. , even in the 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. While the energy-momentum with diagonal components alone allows only locally rotational symmetry, say , in this case there might be a second case with . It was found that, like a Bianchi type-IX case, a positive gives rise to an oscillatory mode of expansion, while a trivial leads to rapid expansion at the early stage of evolution.