The origin of negative pressure fluid (the dark energy) is investigated in the quantum model of the homogeneous, isotropic and closed universe filled with a uniform scalar field and a perfect fluid which defines a reference frame. The equations of th
e model are reduced to the form which allows a direct comparison between them and the equations of the Einsteinian classical theory of gravity. It is shown that quantized scalar field has a form of a condensate which behaves as an antigravitating medium. The theory predicts an accelerating expansion of the universe even if the vacuum energy density vanishes. An antigravitating effect of a condensate has a purely quantum nature. It is shown that the universe with the parameters close to the Planck ones can go through the period of exponential expansion. The conditions under which in semi-classical approximation the universe looks effectively like spatially flat with negative deceleration parameter are determined. The reduction to the standard model of classical cosmology is discussed.
The exactly solvable quantum model of the homogeneous, isotropic and closed universe in the matter-energy production epoch is considered. It is assumed that the universe is originally filled with a uniform scalar field and a perfect fluid which defin
es a reference frame. The stationary state spectrum and the wave functions of the quantum universe are calculated. In this model the matter-energy in the universe has a component in the form of a condensate of massive zero-momentum excitation quanta of oscillations of primordial scalar field. The mean value of the scale factor of the universe in a given state is connected with the mass of a condensate by a linear relation. The nucleation rate of the universe from the initial cosmological singularity point is calculated. It is demonstrated that the process of nucleation of the universe can have an exponential (explosive) nature. The evolution of the universe is described as transitions with non-zero probabilities between the states of the universe with different masses of a condensate.
It is shown that the homogeneous and isotropic Universe is spatially flat in the limit which takes into account the moments of infinitely large orders of probabilistic distribution of a scale factor with respect to its mean value in the state with la
rge quantum numbers. The quantum mechanism of fine tuning of the total energy density in the Universe to the critical value at the early stage of its evolution is proposed and the reason of possible small difference between these densities during the subsequent expansion is indicated. A comparison of the predictions of the quantum model with the real Universe is given.
