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).
