In the theory of massive gravity, suppose that two bodies start interacting by exchanging gravitons. Wouldn't these gravitons, having mass, have to exchange gravitons between themselves, with these new gravitons having to exchange more gravitons, thereby leading to infinite recursion?
I understand the range argument for massless gravitons, as explained here, but I don't understand if gravitons have mass how this seeming paradox related to infinite recursion is resolved conceptually?
In the link you provide, the limit for the mass of the graviton is, after the discovery of the gravitational waves by LIGO as
g < $7.7×10^{−23}$ eV/c2
Such a tiny mass, together with the tiny coupling constant associated with gravity, compared to 1 for the strong interaction , 1/137 for electromagnetism, $ 6x10^{-39}$ for gravity
would ensure that what you fear in calculation would be infinitessimally small.
Wouldn't these gravitons, having mass, have to exchange gravitons between themselves, with these new gravitons having to exchange more massive gravitons, thereby leading to infinite recursion
These gravitons have a fixed mass, as far as I can tell, there are no "more massive gravitons".
By the time a graviton would exchange a graviton with a graviton, it will have flown off to infinity, or been absorbed by some massive body. Such a small mass is practically zero.
The answer to the title question :
Would a massive graviton emit more massive gravitons?
A graviton need not have mass to emit gravitons, because it is a general relativity object which is described by an energy momentum vector which is affected by the space time tensor, as the answer here discusses.
It is the couplings that are so tiny that the mathematical analogy with the strong force cannot generate similar effects within observable times and spaces in our universe.
