  The formula describing the explicit red-shift dependence for the distance
covered by a signal in the expanding space, and also the expressions for Hubble
law have been derived directly from the conformal group transformations taking
into account the light-cone equation. The obtained relations are associated
with the luminosity distance represented as an explicit function of the red
shift involving no other parameters but the scaling factor $c H^{-1}_0$. These
relations represent in a pure kinematical way and in a complete agreement with
observations, the revealed transition of the Metagalaxy to accelerated
expansion (the dark energy effect).
