In a 2003 review Burgess outlined how the QFT perturbative methodology is being extended to gravity, and described some effective quantum gravity expansions that reproduce general relativity in the lowest order, and provide quantum corrections. My question is what were the developments during the last decade, and what remaining issues prevent including such effective quantum gravity into the Standard Model on the same terms as say QCD?
Of course, gravity is non-renormalizable, but after Weinberg renormalizability is considered a mathematical convenience rather than a must, it is nice to have, but... In both renormalizable and non-renormalizable theories it is the cutoff that removes the divergencies and blocks high energy degrees of freedom, whose "true" theory is unknown. Burgess writes that "non-renormalizable theories are not fundamentally different from renormalizable ones. They simply differ in their sensitivity to more microscopic scales which have been integrated out".
One problem with the older semi-classical gravity was that when one couples quantum fields to the classical metric tensor of general relativity it becomes possible to track quantum observables through changes in the tensor, so the uncertainty principle is violated. Conservation laws are also violated, see e.g. Rickles (p.20). Does effective quantum gravity avoid these problems? Burgess also mentions that even the leading quantum corrections might be too small to detect. Is it still the case, and is that where the main problem is?
EDIT: Low Energy Theorems of Quantum Gravity from Effective Field Theory (2015) by Donoghue and Holstein seems to be relevant, it draws direct analogy to QCD:"In QCD at the lowest energies there exist only light pions which are dynamically active and the interactions of these pions are constrained by the original chiral symmetery of QCD. The resulting effective field theory — chiral perturbation theory — has many aspects in common with general relativity". But they only treat gravitational scattering.
