Eddington-Born-Infeld theory and the dark sector

I consider a unified description of the phenomena of dark matter and dark energy which is given by a simple modification of gravity. Gravity is modified with new degrees of freedom which come from a second connection, different from the usual Levi-Civita connection. A candidate action, the Eddington-Born-Infeld action (EBI) for these degrees of freedom was proposed by Bañados and is shown to be dual to a theory with two metrics called bi-gravity. This modification directly gives solutions to the field equations which mimic dark matter for spherically symmetric systems while for cosmological spacetimes it gives, in addition, the effect of dark energy. I shall further show that the effect of dark matter is present even at the linearized cosmological level and that this makes it in harmony with all known large scale cosmological observations.