  The description of the cosmological expansion and its possible local
manifestations via treating the proper conformal transformations as a
coordinate transformation from a comoving Lorentz reference frame to an
uniformly accelerated one is given. The explicit form of the conformal time
inhomogeneity is established. The expression defining the location cosmological
distance in the form of simple function on the red shift is obtained. By
coupling it with the relativistic formula for the longitudinal Doppler effect,
the explicit expression for the Hubble law is obtained, which gives rise to the
connection between acceleration and the Hubble constant. The expression
generalizing the conventional Hubble law reproduces kinematically the
experimentally observed phenomenon treated conventionally as a Dark Energy
manifestation. The conformal time deformation in the small time limit leads to
the quadratic time nonlinearity. Being applied to describe the location-type
experiments, this predicts the existence of the universal uniformly changing
blue-shifted frequency drift. The obtained formulae reproduce the Pioneer
Anomaly experimental data.
