Bianchi type-I cosmology with scalar and spinor fields

We consider a self-consistent system of interacting spinor and scalar fields within the framework of a Bianchi type-I (BI) cosmological model filled with perfect fluid. The interacting term in the Lagrangian is chosen in the form of derivative coupling, i.e., Lᵢₙₜ=(λ/2)φ_,αφ^,αF. Here F is a power or trigonometric function of the invariants I and/or J constructed from bilinear spinor forms S=ψψ and P=iψγ⁵ψ. Self-consistent solutions to the spinor, scalar, and BI gravitational field equations are obtained. The problems of an initial singularity and the asymptotically isotropization process of the initially anisotropic space-time are studied. The role of the cosmological constant (Λ term) in the evolution of a BI Universe is studied. It is shown that a positive Λ generates an oscillatory mode of expansion of the BI model, whereas if F in Lᵢₙₜ is chosen to be a trigonometric function of its arguments, there exists a nonexponential mode of evolution even with a negative Λ. It is shown also that for a suitable choice of problem parameters the present model allows regular solutions without a broken dominant energy condition.