MATHEMATICAL AND GENERAL PHYSICS NONLINEAR SPINOR FIELD IN BIANCHI TYPE-I UNIVERSE FILLED WITH VISCOUS FLUID: SOME SPECIAL SOLUTIONS

Abstract. We consider a system of nonlinear spinor and a Bianchi type I gravitational fields in presence of viscous fluid. The nonlinear term in the spinor field Lagrangian is chosen to be λF, with λ being the self-coupling constant and F being a function of the invariants I an J constructed from bilinear spinor forms S and P. We consider the cases when F is the power law of its arguments. Self-consistent solutions to the spinor and BI gravitational field equations are obtained in terms of τ, where τ is the volume scale of BI universe. System of equations for τ and ε, where ε is the energy of the viscous fluid, is deduced. This system is solved for some special cases. Key words: spinor field, Bianchi type I (BI) model, cosmological constant. PACS numbers: 03.65.Pm and 04.20.Ha I