Self-consistent solutions to the nonlinear spinor field equations in general relativity are studied for the case of Bianchi type-I ͑BI͒ space-time. It is shown that, for some special type of nonlinearity the model provides a regular solution, but this singularity-free solution is attained at the cost of breaking the dominant energy condition in the Hawking-Penrose theorem. It is also shown that the introduction of a ⌳ term in the Lagrangian generates oscillations of the BI model, which is not the case in the absence of a ⌳ term. Moreover, for the linear spinor field, the ⌳ term provides oscillatory solutions, which are regular everywhere, without violating the dominant energy condition.
Within the scope of Bianchi type VI (BVI) model the self-consistent system of nonlinear spinor and gravitational fields is considered. Exact self-consistent solutions to the spinor and gravitational field equations are obtained for some special choice of spatial inhomogeneity and nonlinear spinor term. The role of inhomogeneity in the evolution of spinor and gravitational field is studied. Oscillatory mode of expansion of the BVI universe is obtained for some special choice of spinor field nonlinearity.
We consider a system of interacting spinor and scalar fields in a gravitational field given by a Bianchi type-I cosmological model filled with perfect fluid. The interacting term in the Lagrangian is chosen in the form of derivative coupling, i.e., L int = λ 2 ϕ ,α ϕ ,α F, with 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 or trigonometric functions of its arguments. Self-consistent solutions to the spinor, scalar and BI gravitational field equations are obtained. The problems of initial singularity and asymptotically isotropization process of the initially anisotropic space-time are studied. It is also shown that the introduction of the Cosmological constant (Λ-term) in the Lagrangian generates oscillations of the BI model, which is not the case in absence of Λ term. Unlike the case when spinor field nonlinearity is induced by self-action, in the case in question, wehere nonlinearity is induced by the scalar field, there exist regular solutions even without broken dominant energy condition.
We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy given by a cosmological constant. The perfect fluid is chosen to be the one obeying either the usual equation of state, i.e., p = ζε, with ζ ∈ [0, 1] or a van der Waals equation of state. Role of the Λ term in the evolution of the BI Universe has been studied.
We study the evolution of a homogeneous, anisotropic Universe given by a Bianchi type-I cosmological model filled with viscous fluid, in the presence of a cosmological constant Λ. The role of viscous fluid and Λ term in the evolution the BI space-time is studied. Though the viscosity cannot remove the cosmological singularity, it plays a crucial part in the formation of a qualitatively new behavior of the solutions near singularity. It is shown that the introduction of the Λ term can be handy in the elimination of the cosmological singularity. In particular, in case of a bulk viscosity, it provides an everlasting process of evolution (Λ < 0), whereas, for some positive values of Λ and the bulk viscosity being inverse proportional to the expansion, the BI Universe admits a singularity-free oscillatory mode of expansion. In case of a constant bulk viscosity and share viscosity being proportional to expansion, the model allows oscillatory mode accompanied by an exponential growth even with a negative Λ. Space-time singularity in this case occurs at t → −∞.
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