Is quantum gravity consistent with the principles of equivalence and relativity? I saw an article about physicist testing quantum mechanics in accelerated frames, hoping for insights into quantum gravity. And then I suddenly wondered, is quantum gravity inconsistent with general relativity at the most basic level of the principles of equivalence and relativity?
In general relativity we have the equivalence of a particle at rest on the earth and inside an accelerating rocket, the equivalence of a stationary observer viewing a falling particle and a stationary particle being viewed by an accelerated observer (e.g. an accelerated rocket in special relativity has much of what we call gravity). But a gravitational interaction mediated by gravitons must occur in deBroglian chunks. Like electrons going through the magnets of an accelerator-- rather than accelerating smoothly they're either kicked or not kicked (speaking loosely), and that matters in the design.
So, like, thinking of the "scattering" of a particle under gravity versus moving inertially in an accelerating rocket. Overlooking the weakness of the interaction, it seems like the particle might be kicked by gravity in a way that it wouldn't if it's just sitting there while the rocket accelerates around it.
 A: This is a question that has to wait for the definitive quantization of gravity. And in this case , it would not be definitive if, in the phase space region of overlap with special relativity and classical General Relativity ,it would give different results.
At the moment gravitons are invented so that gravitational interactions will be analogous to the other three interactions, weak, strong , electromagnetic, but the theories are effective, not rigorous.Effective theories are useful for cosmological models but there are infinities in the calculations that cannot be taken into account with renormalization. 
The mathematically rigorous string theories have a niche for the proposed graviton. But it is a theory that depends on all particles being resonances on a string, and no definitive string theory has been proposed so as to go further and check the points you are making. Let alone that it is superstring theories that can accommodate all 
particle and  forces.
AFAIK the ongoing research on quantum gravity  has not reached the point of checking acceleration with rockets.
In addition

But a gravitational interaction mediated by gravitons must occur in deBroglian chunks.

This is a misunderstanding. Interactions happen with the exchange of off mass shell, photons,for electromagnetic, bosons for weak, and gluons for strong. Off mass shell means that their four vectors are exchanged in the interaction and are continuous under the integral which describes the interaction. No chunks of energy. Chunks only happen when it happens that an incoming photon has the energy to change a bound state from one energy level to another, or when a bound state relaxes to a lower energy level emitting a photon. There are no bound states with just gravity.
