Non-local gravity
Although certainly problematic in fundamental theories, one should not exclude the appereance of nonlocalities in effective descriptions of gravity. Nonlocal modifications of General Relativity constructed out of inverse differential operators give rise to infrared effects that could become relevant at large temporal and spatial scales. The consequences of these nonlocalities could be far-reaching and provide a dynamical explanation for dark energy.
Selected paper(s) on this topic:
http://inspirehep.net/record/1469212
http://inspirehep.net/record/1490002