Negative mass hypothesis in cosmology and the nature of dark energy

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The observed acceleration of the universe arises a puzzling question. What is the nature of a dark energy that would cause this phenomenon? We recall the arguments against the existence of negative matter on General Relativity grounds. They vanish if the universe is considered as a manifold M4 associated to two coupled metrics, solutions of a coupled field equation system. We build a non-steady solution where the positive species accelerates while the negative one decelerates. So that dark energy is replaced by (dominant) negative matter action.