2007, Vol.14, pp.250-261

It is shown that the phenomenon of the Universe acceleration and the Pioneer Anomaly can be explained as a purely kinematic consequences of the SO(4,2) conformal group transformations treated as the coordinate transformations from the local Lorentz reference frame to the uniformly accelerating one.
It is shown that special conformal transformations, which preserving the light cone equation, nevertheless brings into existence the nonlinear transformation of its generating lines (conformal deformation of time or the time inhomogeneity). The explicit expression defining the location cosmological distance R(z) and for the ratio =V(z)/R(z) are obtained. It reproduce in the limit z0 the conventional form of the Hubble law. The connection between acceleration and the Hubble constant follows herefrom immediately.
The expression describing the conformal time deformation in the small time limit predict the existence of the uniformly changing blue-shifted frequency drift. Its magnitude is connected with the Hubble constant according to =H₀t(where is the frequency of the signal emitted, t is the time of the signal propagation from the emitter to the receiver). The obtained formulae reproduce the PA experimental data. The function =V(z)/R(z) generalizing the conventional expression for the Hubble law possesses a maximum at the point z₀0.475. That, in fact, reproduce 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.
Key words: Universe acceleration, Pioneer Anomaly, conformal transformations, time inhomogeneity

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