  Introducing a fundamental constant of nature with dimensions of acceleration
into the theory of gravity makes it possible to extend gravity in a very
consistent manner. At the non-relativistic level a MOND-like theory with a
modification in the force sector is obtained, which is the limit of a very
general metric relativistic theory of gravity. Since the mass and length scales
involved in the dynamics of the whole universe require small accelerations of
the order of Milgrom's acceleration constant a_0, it turns out that the
relativistic theory of gravity can be used to explain the expansion of the
universe. In this work it is explained how to use that relativistic theory of
gravity in such a way that the overall large-scale dynamics of the universe can
be treated in a pure metric approach without the need to introduce dark matter
and/or dark energy components.
