Quantum geometrodynamical description of the dark sector of the matter-energy content of the universe

Abstract: The evolution of the universe is studied in exactly solvable dynamical quantum model with the Robertson-Walker metric. It is shown that the equation of motion which describes the expansion or contraction of the universe can be represented in the form of the law of conservation of zero total energy for a particle with arbitrary mass being an analogue of the universe. The analogue particle moves in the potential well under the action of the internal force produced by the curvature of space, matter, and pressures of classical and quantum gravitational sources. At a definite stage of the evolution of the universe, this force can perform the positive work on the universe, which is similar to the work of the repulsive forces of dark energy, or it does the negative work analogous to the work of the attractive forces of dark matter. The cases of real and complex state vectors which describe the geometrical properties of the universe filled with dust and radiation are considered. It is shown that predictions of the quantum model do not contradict the observational data about the accelerating expansion of our universe.