Although the transition from an initially decelerated to a late-time accelerating cosmic expansion is becoming observationally established, the duration of the accelerating phase depends on the cosmological scenario and, several models, which includes our standard one, imply an eternal acceleration or even an accelerating expansion until the onset of a future cosmic singularity. In this regard, an interesting theoretical question arises if one tries to reconcile the standard description of the current cosmic acceleration with the only candidate for a consistent quantum theory of gravity we have today, i.e., Superstring theory.