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Self-consistent system of nonlinear spinor field and Bianchi I (BI)gravitational one with time dependent gravitational constant ($G$) andcosmological constant ($\Lambda$) has been studied. The initial and theasymptotic behaviors of the field functions and the metric one have beenthoroughly investigated. Given $\Lambda = \Lambda_0/\tau^2$, with $\tau =\sqrt{-g}$, $G$ has been estimated as a function of $\tau$. The role of perfectfluid at the initial state of expansion and asymptotical isotropization processof the initailly anisotropic universe has been elucidated.Comment: 7 pages, RevTe

DIRAC SPINOR IN BIANCHI-I UNIVERSE WITH TIME-DEPENDENT GRAVITATIONAL AND COSMOLOGICAL CONSTANTS