  We deduce Tolman's formula of luminosity-distance in Cosmology from
Poincare's definition of light-distance with Lorentz Transformation (LT).In
Minkowskian metric, if distance is proper time (as it is often argued) then
light-distance must be also the shortest distance, like proper duration (unlike
Einstein's longest length within rest system). By introducing Poincare's proper
light-distance in Einstein's basic synchronization we deduce a dilated distance
between observer and receding mirror (with relativistic Doppler factor). Such a
distance corresponds not to an Euclidean distance (Einstein's rigid rod) but to
an Hyperbolic distance (Cayley-Klein) with a Lobatchevskian Horizon. From a
basic proportionality hyperbolic distance-velocity, we deduce the law of
Hubble. By following Penrose's Lobatchevskian representation of LT, we
transform Special Relativity (SR) into an Hyperbolic Cosmological Relativity
(HCR). by using only the LT but the whole LT. In Hyperbolic Rotation motion
(basic active LT or Einstein's boost), Hubble constant (hyperbolic angular
velocity) is coupled with a minimal Milgrom's basic proper acceleration
(hyperbolic centrifugal acceleration).
