Currently the two definitive papers are 1004.1780 and 1010.1939, with several others applying spinfoams to cosmology e.g. 1003.3483. LQG is about where one could have predicted back in Fall 2008, with the merger of the canonical, covariant, and cosmological versions. I think in fact one or more people here at PF did observe that trend and predict that. It unifies the theory and brings it closer to testability, because early-universe cosmology is a potential venue for testing. The present form of LQG is at the intersection of lines of work by Ooguri, Atiyah, Feynman, Regge, Penrose. The October paper mentions that it follows from 3 separate approaches: 1. Canonical quantization of the conventional phase space of General Relativity 2. Polyhedral quantum geometry 3. Covariant lattice quantization For details, see 1010.1939 Thus there are signs that the present form of LQG is a satisfactory theory of quantum geometry/gravity without matter. Matter still has to be introduced. So the question concerns the logical next step. Assuming that what we see will turn out to be satisfactory, how can matter be laid on to the spacetime foundation it provides? At first sight, in the one-page formulation given in the October paper, you see a list of FEYNMAN RULES GOVERNING TWO-COMPLEXES. There is a half-page section on page 1 of 1010.1939 called "Feynman Rules" which at the end says "This completes the definition of the model." The 4 Feynman rules determine how to calculate transition amplitudes, for the two-complexes. That defines LQG. So at first sight, and this may be correct as well, the theory is a theory of two-complexes, so if matter is to be added to the picture it must carried by the two complexes. That's one possibility. I'd like to hear any ideas about how this could be done, or about other schemes for including matter.