Question

I wondered what proof exist for the existence of gravitons?

Answer 1

Therefore, we must prove the graviton existence indirectly (including graviton interaction with a photon). But there is also a major ...

Answer 2

There is quite rigorous proof for the existence of gravitons. It's just that there exists an ad hoc rule that is not based on physics, that a particle can only be "officially" detected in traditional experiments (bubble chambers etc.) and that is just not going to happen for gravitons. However, if you write down a theory where gravity is classical then this will necessarily be in conflict with so many things that it is immediately falsified. So, in that sense, the non-existence of gravitons can be said to have been experimentally falsified.