Classical and Quantum Evolution of the Bianchi Type I Model

Abstract

The classical and quantum evolution of an anisotropic cosmological Bianchi type I model is considered. In the classical case, the influence of the minimally coupled scalar field is taken into account. Thus the system of two equations is obtained, which are explored at the inflationary and scalaron stages. The quantum problem in view of the positive cosmological constant is considered. The principal moment of the account of an anisotropy is the occurrence of the potential barrier unbounded in zero and at infinity. Though the greatest value of the potential is less than zero and the total energy of the Universe E=0, there is an important opportunity for above-barrier reflection of the wave function of the Universe. After reflection the wave function describes the expanding Universe promptly losing anisotropy and transferring into the Friedmann Universe.