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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.

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    $\begingroup$ The point of renormalization is not simply to remove divergences but to gain a model that is described by a finite number of physically meaningful parameters. A model that can paint a duck in the detector today and a crocodile tomorrow is completely useless. If what you end up with at the end of the day is a forcefully regularized model with a cutoff, that's nothing else than the admittance that you have absolutely no idea what is really going on while you are shoehorning. $\endgroup$ – CuriousOne Jan 16 '16 at 2:06
  • $\begingroup$ @CuriousOne Nonetheless non-renormalizable theories are now routinely admitted, and even renormalizable ones are known to have non-renormalizable low-energy reductions, so there is no avoiding them. If I understand Cao and Burgess correctly restrictions on effective theories that make them physically sensible are far broader than renormalizability, and in EQG in particular the terms of perturbative expansions are more or less uniquely determined, it is no string theory. $\endgroup$ – Conifold Jan 16 '16 at 3:42
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    $\begingroup$ Fermi's theory of CP violating weak interactions is non-renormalizable, it was experimentally confirmed. And "low energy effective theory" is a standard term in physics as you well know. Is there a point to this? $\endgroup$ – Conifold Jan 16 '16 at 5:05
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    $\begingroup$ @Lewis Miller I thought that people do not believe that renormalizable gravity is promising, both string theory and LQG are looking for a "final" theory not in QFT form. But so far they face a lot of issues, it seems that this low energy effective gravity might be a bridge to resolving some of them in simpler context. $\endgroup$ – Conifold Jan 19 '16 at 1:04
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    $\begingroup$ see also this discussion: physicsforums.com/posts/5338754 $\endgroup$ – Arnold Neumaier Jun 29 '16 at 11:56
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There is a recent survey of canonical quantum gravity and its confrontation with exciting experimental data:

R.P. Woodard, Perturbative Quantum Gravity Comes of Age, Int. J. Modern Physics D 23 (2014), 1430020. http://arxiv.org/abs/1407.4748.

Woodard writes in the introduction:

All of the problems that had to be solved for flat space scattering theory in the mid 20th century are being re-examined, in particular, defining observables which are infrared finite, renormalizable (at least in the sense of low energy effective field theory) and in rough agreement with the way things are measured. [...] The transformation was forced upon us by the overwhelming data in support of inflationary cosmology.

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    $\begingroup$ Great survey! Conclusions outline the remaining challenges, e.g. "some people dismiss the impact of inflationary cosmology on quantum gravity because the detection of primordial gravitons is still tentative and because fundamental theory has yet to provide a compelling model of primordial inflation... The six fine tuning problems I mentioned in section 3.1 indicate that there is something very wrong with our current thinking. I suspect only a painful collision with data is going to straighten us out". $\endgroup$ – Conifold Jul 5 '16 at 22:48

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