The General Relativity (GR) surely the most elegant theory in our possession, in spite of the recent measurement of Gravitational waves, has not yet been quantized and requires, in order to be compatible with cosmological observations, very unnatural hypotheses. Other theories came on age (MOND, Milne-Universe, etc.) but they do not seem to answer all the questions. On another side the very presence of negative energy solutions in Quantum Equations has always required an interpretation of the negative masses. What would be the scenario if we simply considered repulsive the gravitational interaction between "positive" masses and "negative" masses, between matter and antimatter? Various questions are proposed: A) A repulsive gravitational interaction is compatible with the elegant apparatus of the RG? B) Does a repulsive gravitational relationship generate at least one measurable phenomenon (contribution to CPV) in a viable experimental system? We propose an experimental test of the gravitational interaction with antimatter by measuring the branching fraction of the CP violating decay of KL in space or on the Moon. A 5 sigma discrimination may be obtained by collecting the KL produced by the cosmic proton flux within a few years. C) A repulsive gravitational relationship generates phenomena and suggests new modalities that can be the basis of an elegant alternative to "Dark Matter" and "Dark Energy".