  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.
