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Well, its a geometric deformation of space-time because the displacement by mass
Depends on your definition. If you stop at quantum mechanics way of defining a force with boson exchange then you may also say gravity doesn't exist, because it's not included in the standard model for now.
Well, firstly, we can quantize gravity pretty easily, it just has unphysical divergences.
But secondly, I think it makes most sense to talk about the current accepted physics because we don't know how quantum gravity will work.