http://arxiv.org/abs/1508.04641 The body text of the paper ends up calling the "Hybrid metric-Palatini gravity theory" f(X) gravity. From the body text (citations and internal references omitted without notation): The paper closes by identifying many issues for further study and arguing that the effort to do so would be worthwhile. This is a classical modified GR theory, not a quantum gravity theory. But, the fact that a term in the form of a Yukawa potential naturally arises in the f(X) formulation is suggestive of the notion that f(X) gravity might be the classical limit of a quantum gravity theory with a non-trivial self-interaction term. While f(R) gravity theories and Palatini gravity theories have each been studied extensively in isolation, the f(X) gravity hybrid is a new car that has only been on a small number of test drives. Equations that seem to make sense have been derived to address both dark energy and dark matter phenomena with this theory (and it may be able to provide guidance on the issue of inflation as well), but no one has plugged in numbers and rigorously compared the performance of f(X) gravity to other modified gravity theories or to lamdaCDM relative to the empirical evidence. Several specific realistic to conduct observational tests of the theory have been suggested, but none have actually been conducted.