  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 (RF) to an
uniformly accelerated RF is given. The explicit form of the conformal
deformation of time 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 well known relativistic formula defining the
relative velocity of the mutually moving apart source and receiver of the
signal, the explicit analytic expression for the Hubble law is obtained. The
connection between acceleration and the Hubble constant follows therefrom
immediately. The expression for 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 uniformly
changing blue-shifted frequency drift. Phenomenon of the Pioneer Anomaly (PA)
is treated as the first of such a kind of effects discovered experimentally.
The obtained formulae reproduce the PA experimental data. The expression
generalizing the conventional Hubble law reproduces the experimentally observed
phenomenon which in the frame of the conventional cosmological paradigm is
treated as the transition from the decelerated expansion of the Universe to the
accelerated one.
