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 ($\mathrm{\Lambda }$) has been studied. The initial and the asymptotic behaviors of the field functions and the metric one have been thoroughly investigated. Given $\mathrm{\Lambda }={\mathrm{\Lambda }}_0\mathrm{/}{\tau }^2$, with $\tau = \sqrt{-g}$,$G$hasbeenestimatedasafunctionof$\tau$. The role of perfect fluid at the initial state of expansion and asymptotical isotropization process of the initailly anisotropic universe has been elucidated.