| Abstract: | A Bianchi I model of the Universe filled with interacting nonlinear spinor and scalar fields is studied within quantum geometrodynamics. Three types of interaction are considered: gradient, Yukawa, and axion ones. For massless fermion fields, the variables in the Wheeler – de Witt equation will separate. The solution can be interpreted using a two-component perfect liquid. One component corresponds to a massless scalar field, while the other – to a nonlinear spinor field. The interaction between the spinor and scalar fields can lead to elimination of singularity of the wave function. There is a possibility of existence of a discrete spectrum of the quantum Universe, as well as tunneling from the region with a rigorous equation of state to the region of the de Sitter vacuum. |
