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 = root -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 initially anisotropic universe has been elucidated.