It's often been hoped that gravity is topological, eg. Witten, Xu, Gu & Wen, Rovelli. Heckman & Verlinde make a new suggestion: http://arxiv.org/abs/1112.5210 Instantons, Twistors, and Emergent Gravity "The basic idea is to view N = 4 gauge theory on S4 as an effective low energy description of an underlying topological large N gauge theory, without any local propagating degrees of freedom." Interestingly, they say their model has some similarities to an earlier condensed matter model by Zhang and Hu, which Gu and Wen also refer to: http://arxiv.org/abs/cond-mat/0110572 A Four Dimensional Generalization of the Quantum Hall Effect "On the other hand, the main problem with the current model seems to be the “embarrassment of riches”. ... As a result, there are not only photons and gravitons in the collective modes spectrum, there are also other massless relativistic particles with higher spins."