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

Abstract

We generalize tensor–scalar theories of gravitation by the introduction of an ‘abnormallyweighting’ type of energy. This theory of tensor–scalar anomalous gravity is based on arelaxation of the weak equivalence principle that is currently restricted to ordinary visiblematter only. As a consequence, the mechanism of convergence toward generalrelativity is modified and produces cosmic acceleration naturally as an inescapablegravitational feedback induced by the mass variation of some invisible sector. Thecosmological implications of this new theoretical framework are studied. From theHubble diagram cosmological test alone, this theory provides estimates of theamount of baryons and dark matter in the Universe that are consistent with theindependent cosmological tests of the cosmic microwave background and big bangnucleosynthesis. Cosmic coincidence is naturally achieved from an equally naturalassumption on the amplitude of the scalar coupling strength. Finally, from theadequacy for supernovae data, we derive a new intriguing relation between thespace–time dependences of the gravitational coupling and the dark matter mass,providing an example of a crucial constraint on microphysics from cosmology. Thisprovides glimpses of an enticing new symmetry between the visible and invisiblesectors, namely that the scalar charges of visible and invisible matter are exactlyopposite.