In a previous paper, we demonstrated that the linearized general relativity could explain dark energy (the experimental values of parameters ΩΛ, the cosmological constant, the recent acceleration of the expansion of our Universe) offering an amazing image of our universe at an incredible scale. This explanation of dark energy relies on the assumption of the existence of a negative gravitational mass (with always a positive inertial mass meaning that gravitation could be repulsive). This article demonstrates that this assumption is not only compliant with general relativity but even that the repulsive gravitational interaction is inscribed in the equations of the general relativity. The absence of negative gravitational mass should then be justified because nothing forbids its existence and until now repulsive gravitation has never been observed. This natural possibility of general relativity must be then avoided by adding an ad hoc paradigm. In a way, the principle of masses’ equivalence plays indirectly this role. We will show why this principle can be verified with a great accuracy but we also propose experiments that could violate this principle, allowing at the same time rejecting its status of theoretical principle. This frame of explanation (general relativity released from this ad hoc constraint) opened then the way of the negative gravitational mass with its natural corollary, the repulsive gravitational interaction, and of the following major predictions: the antimatter should have a negative gravitational mass, the neutrino should not be a Majorana particle, the principle of equivalence of masses should be violated for the antiprotonic helium, the apparent disappearance of antimatter could be explained. We recall some other consequences: an “initial” cosmic inflation would be unavoidable, dark energy (or cosmological constant) might not be constant in time (causing accelerating universe). Several experiments are testing some of these predictions: NEMO experiment tests if neutrino is a Majorana particle, and AEgIS, ALPHA and GBAR experiments at CERN test the behavior of the gravitational interaction on anti-matter and the sign of its gravitational mass. First results could be obtained in 2018. Experiments are proposed to test the violation of the principle of equivalence of the masses.
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