Maybe “reconciling” isn’t the best word, but I have some basic questions on quantum gravity. Let’s assume, at least initially, that dark matter is really just matter, and MOND is not needed to explain observations.
The most basic question is, with quantum gravity, what is the shape of space? Is it now a flat Minkowski space? You can’t, I would think, have both curved space and gravitons. You’d have just gravitons, and a result that can be very accurately described as curved space in the classical limit, similar to the way you really have individual photons, but they satisfy Maxwell’s equations in the classical limit. You don’t have the classical EM field, and then add in photons on top of that. Or am I way off base here, and gravitons are expected to transmit actual spatial curvature?
Is the graviton (expected to be?) its own antiparticle, like the photon?
What about dark energy? Is there now a new particle required to transmit the dark energy repulsion, or could that also transmitted by the graviton?
You’ve hit on an important problem in quantum gravity!
The simplest path to quantum gravity is to to take the tensor field that describes the geometry of spacetime (i.e. the metric as it is usually, albeit slightly inaccurately, called) and cut it in to two pieces: one background part that describes the geometry of a flat spacetime and one perturbation part that describes the perturbation of the geometry from the geometry of the background flat spacetime. You can then treat the field describing the perturbation as a field in flat spacetime and go about quantitizing it as you would any other field in flat spacetime (e.g. the electromagnetic field).
Unfortunately nothing is that simple and the quantum field theory has the nasty problem of being non-renormalizable which means that it involves terms that blow up to infinity and at present there are no ways to resolve these infinite terms, except for low energy phenomena when they can be ignored. It’s worth noting though that string theory usually takes this approach to gravity (except instead of the background part being Minkowski space, it would be a Calabi-Yau space or some other space that accommodates string theory’s need for extra spacetime dimensions), which offers some hope of getting around the problem of non-renormalizabilty.
There are other reasons too why some physicists find this approach objectionable, the main one being that it lacks a property called “background independence”.
Whilst there is no reason at all that when we cut up spacetime our background part had to be any particular part or even that it had to be flat, the fact that we had to choose a background at all is problematic. Aside from being conceptually very much against the spirit of Einstein’s generally-covariant theory, our final answers for any measurable quantity we care to calculate will have some, sometimes large, degree of dependence on the particular choice of background.
There are some approaches to quantum gravity that are to greater and lesser degrees background independent (though of course no approach to QG yet has produced a theory that is useful enough to be satisfactory), but one big problem is that, without a background where the geometry and even topology is fixed, it is difficult to define a quantum field as you don’t know what you’re defining it on.
Gravitational waves are usually examined in the context of linearized general relativity. This uses a very similar approach as taken above, e.g. you divide the spacetime metric in to a flat part and a perturbation. The advantage of this is that you can ignore the higher terms of the perturbation and in fact it is very difficult to even describe the properties of a gravitational wave unless you view it as the perturbation of a background spacetime.
Gravitons therefore are just the quanta of peturbations of the background spacetime that make up gravitational waves, just as photons are the quanta that make up em waves. So there’s a sort of dual view going on: we are deliberately ignoring to some extent that gravitons are associated with curvature by viewing them in terms of a background spacetime. In fact gravitons fall very naturally out of the approach of dividing the spacetime in to a background and perturbation part and their basic properties can easily be deduced.
Gravitons would be their own antiparticle as applying a CPT transformation to a graviton would yield another graviton.
It really depends what dark energy is. If dark energy is the result of a dark energy field then it presumably can be quantizied like any other field, resulting in a particle that may or may not exist.