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The description of the cosmological expansion and its possible localmanifestations via treating the proper conformal transformations as acoordinate transformation from a comoving Lorentz reference frame (RF) to anuniformly accelerated RF is given. The explicit form of the conformaldeformation of time is established. The expression defining the locationcosmological distance in the form of simple function on the red shift isobtained. By coupling it with the well known relativistic formula defining therelative velocity of the mutually moving apart source and receiver of thesignal, the explicit analytic expression for the Hubble law is obtained. Theconnection between acceleration and the Hubble constant follows therefromimmediately. The expression for the conformal time deformation in the smalltime limit leads to the quadratic time nonlinearity. Being applied to describethe location-type experiments, this predicts the existence of the uniformlychanging 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 expressiongeneralizing the conventional Hubble law reproduces the experimentally observedphenomenon which in the frame of the conventional cosmological paradigm istreated as the transition from the decelerated expansion of the Universe to theaccelerated one.

Accelerating Universe and Pioneer anomaly as manifestation of conformal time inhomogeneity