Dirac Spinor in Bianchi-I Universe with Time Dependent Gravitational and Cosmological Constants

Self-consistent system of nonlinear spinor field and Bianchi I (BI) gravitational one with time dependent gravitational constant ($G$) and cosmological constant ($\Lambda$) has been studied. The initial and the asymptotic behaviors of the field functions and the metric one have been thoroughly investigated. Given $\Lambda = \Lambda_0/\tau^2$, with $\tau = \sqrt{-g}$, $G$ has been estimated as a function of $\tau$. The role of perfect fluid at the initial state of expansion and asymptotical isotropization process of the initailly anisotropic universe has been elucidated.