  It has been demonstrated that a modern stage of the Universe expansion may be
described in accordance with the observations within the scope of the
space-time conformal geometry. The clock synchronization procedure in SR has
been generalized to the case of the expanding space. It has been found that a
universal local manifestation of the cosmological expansion is a background
acceleration, the value of which is determined by Hubble constant. The formulae
defining an explicit red-shift dependence of the cosmological distance and
expressions for Hubble law have been obtained in a pure kinematic way from the
conformal group transformation, providing a quantitative representation of the
Pioneer anomaly and of the effect associated with the experimentally revealed
Metagalaxy transition to its accelerated expansion
