KurtLudwig said:
When there will be a quantum gravity theory, it must involve a boson, such as the hypothesized graviton
This is not necessarily true as a statement about the fundamental theory. We think it's true that any quantum gravity theory will have to have some
approximation in which it can be viewed as a quantum field theory of a massless spin-2 field. But that doesn't mean that QFT has to be the fundamental quantum gravity theory.
Further discussion of this topic should be in a new thread since this is not the right forum for it. See further comments below.
KurtLudwig said:
to interact with protons and neutrons.
Why are you picking out protons and neutrons particularly? Gravity interacts with everything.
KurtLudwig said:
Protons and neutrons do have cross sections, 10^-15m.
The term "cross section" has a particular technical meaning in physics, and it's not what you appear to be thinking.
Protons and neutrons can, for many purposes, be modeled as having fairly sharp boundaries at around the distance scale you give. However, this is just a model and doesn't work for all purposes, nor do we have any way AFAIK of deriving such a result from first principles.
However, the cross section of protons and neutrons for
interacting with each other or with other particles can vary widely, depending on the type of interaction. It is certainly not always the equivalent of a distance scale of ##10^{-15}## meters.
KurtLudwig said:
To interact, I assume that a graviton will have a cross section too.
In the technical sense I just described, we would expect to be able to calculate interaction cross sections for the graviton with various other particles, yes. But in the sense you were using the term, as some kind of "size" of a boundary, a graviton, or indeed any massless particle, can't have a well-defined size. (The technical reason for this is that massless particles cannot be localized the way massive particles can; more precisely, Newton-Wigner localization doesn't work for massless particles.)
KurtLudwig said:
I do not see how the 1/r^2 law can reduce the cross section of a proton while it reacts with a graviton.
The 1/r^2 law has nothing whatever to do with cross sections, either in your sense of the size of a "boundary" for a particle, or in the more correct sense of interaction cross sections. It's a classical approximation that's only valid in certain regimes, and that views the interaction as a force between objects that are considered point particles for purposes of the approximation. If you're trying to view the interaction as an exchange of virtual particles, you're not using the classical model of force at all, and trying to mix them together won't work, it will just confuse you.
KurtLudwig said:
Then the frequency of the gravitational reactions will only depend on the time it takes the gravitons to reach these protons of the hydrogen gas. Since this is time related, the frequency of interactions will be proportional to 1/r from the source of the gravitons. The source being a nearby star.
This is all personal theory and is out of bounds for discussion here.
If you want to discuss the classical models of gravity that are used to study galaxies, galaxy clusters, and the like in cosmology, that is what this thread would be appropriate for. Trying to investigate quantum gravity models has nothing whatever to do with that.
If you want to discuss particular quantum gravity models that appear in the literature, you can start a new thread in the appropriate forum, which would probably be the Beyond the Standard Model forum.
If you want to speculate about your own home-brewed model of quantum gravity, you'll have to go somewhere else; that's not what PF is for.