Gravitons are usually formulated by perturbing the metric around the flat Minkowski metric, but you can do perturbation theory around any metric, include those

Gravitons are usually formulated by perturbing the metric around the flat Minkowski metric, but you can do perturbation theory around any metric, include those that describe accelerating frames. So, you might actually get gravitons in an accelerated frame. What you call background metric and what you call gravitons can get mixed together. However, because gravity is formulated in a generally covariant (ie. invariant under diffeomorphisms) the physical predictions must nevertheless agree when formulated in a frame-independent manner, much as they must in special relativity. Maybe the best example of quantum effects being different for accelerating and stationary observers is the Unruh Effect ( https://en.wikipedia.org/wiki/Unruh_effect https://en.wikipedia.org/wiki/Unruh_effect ). If an observer accelerates relative to a 0-temperature vacuum, they will see a blackbody background with T ~ a.