Coarse graining has become an increasingly important topic in loop quantum gravity with several researchers working on it. As usual in physics, one is interested in integrating out microscopic degrees of freedom and doing computations on an effective coarse level. How exactly the states, observables, and dynamics of the theory should change under such a renormalisation group flow is only poorly understood at the moment.
Recently, I have written a paper about this topic in a simplified context which is tailored to reproduce loop quantum cosmology from loop quantum gravity. Here, one can explicitly coarse grain the relevant observables, the scalar field momentum and the volume of the spatial slice, and check that their dynamics remains unchanged under such a coarse graining.
The reason that this works is rooted in an exact solution to loop quantum cosmology which can be imported in this full theory setting. In particular, the form of the dynamics of this solution is independent of the volume of the universe. It then follows that if we concentrate the volume of some set of vertices at a single one, the evolution of this coarse grained volume will agree with the evolution of the sum of the individual volumes.
The content of the paper is sketched in the brief talk linked above.