Interacting spinor, vector and scalar fields in Bianchi-I space-time: the isotropization problem

Summary: "We consider Bianchi-I type universes with interacting spinor, vector and scalar fields in general relativity. The spinor field Lagrangian contains a nonlinearity in the form of an arbitrary function of the invariant S=overlinepsipsi, while the vector and scalar fields' Lagrangian contains an interaction of the form phi_{,alpha}phi^{,alpha}H(I), H(I) being an arbitrary function of the invariant I=A_beta A^beta. It is shown in a general form that the time-dependent scalar and vector fields are unable to create a model with isotropization at late times, whatever the function H(I), whereas an addition of a spinor field (linear or nonlinear) makes the model isotropize. The set of field equations is entirely integrated with the above arbitrary nonlinearities, and some explicit examples are considered."