Title
Maybe gravitons aren’t affected by gravity, the same way photons aren’t affected by em interactions (which they carry).
If that was the case, we would already have a quantum theory of gravity. The fact that “gravitons” (here I mean the particles of a second quantisation of GR) can interact with themselves makes the theory almost completely useless.
It’s technically possible to write down such a theory, but the only way to get results out of it is to first perform an infinite number of experiments.