arXiv subjects
Publications and source records attributed to V. N. Folomeev.
The quantum evolution of a model of the universe with account of two scalar fields ({\it dilaton} and {\it inflaton}) is considered. For this case, the closed and flat models has been examined. It is shown that in both cases the realization of conditions necessary for inflation is strongly depends on coupling constant for dilaton and inflaton fields.
The behaviour of the flat anisotropic model of the Universe with a scalar field is explored within the framework of quantum cosmology. The principal moment of the account of an anisotropy is the presence either negative potential barrier or positive repelling wall. In the first case occur the above barrier reflection of the wave function of the Universe, in the second one there is bounce off a potential wall. The further evolution of the Universe represents an exponential inflating with fast losses of an anisotropy and approach to the standard cosmological scenario.
The behaviour of the wave function of the Universe under the barrier for anisotropic cosmological Bianchi type IX model with account of influence of the scalar field is explored. In view of known difficulties with interpretation of multidimensional wave functions the method of reduction of such problems to one-dimensional is offered. For this purpose in frameworks of semiclassical approach the system of characteristics equations relative to one variable is written out. This system describe a bundle of the characteristics along which the multidimensional problem is reduced to one-dimensional one that allows to utillize the standard interpretation of the wave function as well as for usual Schrodinger equation. The obtained results for Bianchi type IX model are reduced to the following statement: the Universe tunnels through the barrier from an isotropic state with zero initial value of the scalar field and appear in classically allowed region with small anisotropy that is necessary for providing of long-lived inflation for deriving the Universe such as ours.