Our present understanding of the universe requires the existence of dark matter and dark energy. We describe here a natural mechanism that could make exotic dark matter and possibly dark energy unnecessary. Graviton-graviton interactions increase the gravitational binding of matter. This increase, for large massive systems such as galaxies, may be large enough to make exotic dark matter superfluous. Within a weak field approximation we compute the effect on the rotation curves of galaxies and find the correct magnitude and distribution without need for arbitrary parameters or additional exotic particles. The Tully-Fisher relation also emerges naturally from this framework. The computations are further applied to galaxy clusters.

Version published in Phys. Lett. B. Added material: 1) We explicited the steps leading from the Einstein-Hilbert Lagrangian to our simplified Lagrangian. 2) We showed how the Tully-Fisher relation emerges naturally from our framework. 3) We added a discussion on the approximations we used