The abnormally weighting energy hypothesis:: the missing link between dark matter and dark energy

We generalize tensor-scalar theories of gravitation by the introduction of an 'abnormally weighting' type of energy. This theory of tensor-scalar anomalous gravity is based on a relaxation of the weak equivalence principle that is currently restricted to ordinary visible matter only. As a consequence, the mechanism of convergence toward general relativity is modified and produces cosmic acceleration naturally as an inescapable gravitational feedback induced by the mass variation of some invisible sector. The cosmological implications of this new theoretical framework are studied. From the Hubble diagram cosmological test alone, this theory provides estimates of the amount of baryons and dark matter in the Universe that are consistent with the independent cosmological tests of the cosmic microwave background and big bang nucleosynthesis. Cosmic coincidence is naturally achieved from an equally natural assumption on the amplitude of the scalar coupling strength. Finally, from the adequacy for supernovae data, we derive a new intriguing relation between the space-time dependences of the gravitational coupling and the dark matter mass, providing an example of a crucial constraint on microphysics from cosmology. This provides glimpses of an enticing new symmetry between the visible and invisible sectors, namely that the scalar charges of visible and invisible matter are exactly opposite.