Properties of the quantum universe in quasistationary states and cosmological puzzles

Old and new puzzles of cosmology are reexamined from the point of view of quantum theory of the universe developed here. It is shown that in proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the observed dimensions of nonhomogeneities of matter density and the amplitude of fluctuations of the cosmic background radiation temperature in the Universe and points to a new quantum mechanism of their origin. The large scale structure in the Universe is explained by the growth of nonhomogeneities which arise from primordial quantum fluctuations due to finite width of quasistationary states. The theory allows to obtain the value of the deceleration parameter which is in good agreement with the recent SNe Ia measurements. It explains the large value of entropy of the Universe and describes other parameters.