On possible manifestation of feedback coupling between geometry and   matter in a phenomenon of an accelerating expansion of the Universe
  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. 
V. V. Kuzmichev, V. E. Kuzmichev (Bogolyubov Institute for Theoretical   Physics)