The standard framework "gravity + matter fields" deals with some difficulties which already appear at low energy and therefore are likely to be detached from its UV completion. I will give account of a recent attempt to modify General Relativity (GR) in the infra-red (IR) and address those difficulties. The proposed modification does not contain any adjustable parameter as it is effective at length scales comparable with the inverse curvature. The guiding line for this modification is a recently proposed "ultra-strong" version of the equivalence principle, according to which the vacuum expectation value of the (bare) energy momentum tensor is exactly the same as in flat space: constant everywhere and quartically divergent with the cut-off. It is possible to work out explicitly the first IR-corrections to GR in the case of a Friedman Robertson Walker Universe. I will show that, for a matter dominated universe, the proposed modification goes in the direction of an effective positive acceleration, but it is too mild to explain, on its own, supernovae data.