Bianchi type I cosmology with scalar and spinor fields

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., ${\cal L}_{\rm int} = \fracλ{2} \vf_{,α}\vf^{,α} F$, 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.

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