  It is shown that an accelerating expansion of the present-day Universe
extracted from observed luminosity of the type Ia supernovae can be explained
by quantum theory which takes into account feedback coupling between geometry
and matter (like in Mach's principle). At the same time an accelerating
expansion of the Universe is explained by the influence of small negative
cosmological constant. A comparison with the model with positive cosmological
constant (dark energy) which also has obtained its theoretical grounds in a
structure of the developed formalism is made. Parameters of the Universe in the
states with large quantum numbers are calculated.
