The law of evolution of energy density in the universe imposed by quantum cosmology and its consequences

The quantum model of homogeneous and isotropic universe filled with the uniform scalar field is considered. This model predicts effective inverse square-law dependence of the mean total energy density <\rho> on the expectation value of cosmological scale factor <a> where the averaging is performed over the state with large quantum numbers. Such a law of decreasing of <\rho> during the expansion of the universe allows to describe the observed coordinate distances to type Ia supernovae and radio galaxies in the redshift interval z = 0.01 - 1.8. A comparison with phenomenological models with the cosmological constant (\Lambda CDM) and with zero dark energy component (\Omega_{M} = 1) is made. It is shown that observed small deviations of the coordinate distances to some sources from the predictions of above mentioned simple quantum model can be explained by the fluctuations \delta a of the scale factor about the average value <a>. These fluctuations can arise due to finite widths of quasistationary states in the early universe. During expansion the fluctuations \delta a grow with time and manifest themselves in the form of observed relative increase or decrease of coordinate distances. The amplitudes of fluctuations \delta a/<a> calculated from observed positions of individual supernovae are in good agreement with their estimations in quantum theory. Possible consequences from the conclusions of quantum theory are discussed.