The problem of quantum gravity is impossibly hard because it is too general. Quantum gravity problem is not trivial but not nearly as hard if we consider a static spacetime such as Einstein static model . Quantum field theory on this specific spacetime is essentially a solved problem. In fact, even Euclidean quantum field theory following Osterwalder-Schrader quantization and Wightman axioms has been worked out in this case ( jaffee-ritter-qft1jaffee-ritter-qft2 osterwalder-schrader-2osterwalder-schrader-1 ). In presentations of quantum field theory on curved spacetimes the Einstein static spacetime appears often as a relatively simple example (see Fewster lecturenote-3908 (1)).
The trouble with quantum gravity is that it is only an inaccessibly hard problem because it is the wrong question on arbitrary Lorentzian spacetimes. The problem is a bad cosmology: there is no expansion or any early universe. The problem of quantum gravity is that it is attempting to solve an irrelevant and overly general problem of an expanding spacetime while in fact the problem can be solved when the spacetime is static and globally hyperbolic with a compact Cauchy surface. It is in this setting where quickly we discover that there is no dark energy necessary in the sense that vacuum energy (which is well-defined for static spacetimes not suffering ambiguities of more general Lorentzian situations) is approximately equal to measured cosmological constant. The dark energy is just the curvature of a static universe. If one proceeds by a Wheeler-deWitt equation for quantum gravity, then this can also be solved explicitly via Huen functions etc. Thus specialization of the quantum gravity problem to a specific static spacetime resolves the most pressing issues of quantum gravity. It seems quite dangerous for thousands of physicists getting lost in speculative scenarios which will most likely have the same fate as the thousands of papers on solutions of Einstein equations without physical relevance. The quantum gravity problem is a GLOBAL problem in the sense that it must necessarily be affected by the geometry of the entire cosmos. It will be very unlikely to have a local solution that has merit. The hardness of the problem seems to be due to trying to force local considerations lead to gravity.