Quantum cosmological effects from the high redshift supernova   observations
  Subject of this contribution is to demonstrate that the observed faintness of the supernovae at the high redshift can be considered as a manifestation of quantum effects at cosmological scales. We show that observed redshift distribution of coordinate distances to the type Ia supernovae can be explained by the local manifestations of quantum fluctuations of the cosmological scale factor about its average value. These fluctuations can arise in the early universe, grow with time, and produce observed accelerating or decelerating expansions of space subdomains containing separate supernovae with high redshift whereas the universe as a whole expands at a steady rate. 
V. V. Kuzmichev (Bogolyubov Institute for Theoretical Physics)