MOND as the basis for an extended theory of gravity

This review describes why the geometric nature of space–time, the Einstein equivalence principle, and the geodesic motion of particles show the possibility of building an extended relativistic theory of gravity on regions where the Tully–Fisher law is valid. It is also shown how a metric construction of gravity can have a modified Newtonian dynamics behaviour compatible with the Tully–Fisher law and the bending of light observed in individual, groups, and clusters of galaxies. It is also reviewed how this metric theory of gravity fits reasonably well on cosmological scales explaining the current acceleration of the universe.