The existence of a non-zero cosmological constant Lambda gives rise to controversial interpretations. Is Lambda a universal constant fixing the geometry of an empty universe, as fundamental as the Planck constant or the speed of light in the vacuum? Is it instead something emerging from a perturbative calculus performed on the metric solution of the Einstein equation and to which it might be given a material status of (dark or bright) ``energy"? Since a physical quantity like mass originates in a Minkowskian conservation law, we proceed with a group theoretical interpretation of this relation in terms of the two possible Lambda-deformations of the Poincaré group with maximal symmetry, namely the de Sitter and Anti de Sitter groups. We use the so-called Garidi mass in order to make clear the asymptotic relations between Minkowskian masses m and their possible dS/AdS counterparts. A resulting conjecture on the appearance of  Dark Matter in early period of universe will be presented. 