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Physics of Particles and Nuclei

, Volume 49, Issue 2, pp 146–212 | Cite as

Spinor Field Nonlinearity and Space-Time Geometry

  • Bijan Saha
Article
  • 23 Downloads

Abstract

Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time, though the isotropy of space-time can be attained for a large proportionality constant. As far as evolution is concerned, depending on the sign of coupling constant the model allows both accelerated and oscillatory mode of expansion. A negative coupling constant leads to an oscillatory mode of expansion, whereas a positive coupling constant generates expanding Universe with late time acceleration. Both deceleration parameter and EoS parameter in this case vary with time and are in agreement with modern concept of space-time evolution. In case of a Bianchi type-I space-time the non-diagonal components lead to three different possibilities. In case of a full BI space-time we find that the spinor field nonlinearity and the massive term vanish, hence the spinor field Lagrangian becomes massless and linear. In two other cases the space-time evolves into either LRSBI or FRW Universe. If we consider a locally rotationally symmetric BI(LRSBI) model, neither the mass term nor the spinor field nonlinearity vanishes. In this case depending on the sign of coupling constant we have either late time accelerated mode of expansion or oscillatory mode of evolution. In this case for an expanding Universe we have asymptotical isotropization. Finally, in case of a FRW model neither the mass term nor the spinor field nonlinearity vanishes. Like in LRSBI case we have either late time acceleration or cyclic mode of evolution. These findings allow us to conclude that the spinor field is very sensitive to the gravitational one.

Keywords

Spinor field late time acceleration oscillatory solution anisotropic cosmological models isotropization 

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Laboratory of Information Technologies Joint Institute for Nuclear ResearchDubna, Moscow oblastRussia

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