  The quantum model of the homogeneous and isotropic universe predicts
logarithmic-law dependence of coordinate distance to source on redshift z which
is in good agreement with type Ia supernovae and radio galaxies observations
for the redshift range z = 0.01 - 1.8. A comparison with phenomenological
models with dark energy in the form of cosmological constant and without dark
energy component is made. Fluctuations of the cosmological scale factor about
its average value which can arise in the early universe produce accelerating or
decelerating expansions of space subdomains containing separate sources with
high redshift whereas the universe as a whole expands at a steady rate.
