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According to GR, gravity is just distortions in 4D space-time, so it's not exactly a force. Bosons are basically force carriers, but if gravity isn't a force, then why would it have a force carrier? Then really what we have to do (and is kinda doing) is to make a coordinate system for QFT that doesn't get messed up by GR (not saying that this is easy). Does graviton have to exist because of gravitational energy? If gravity isn't a force but can do work, it really seems to be pulling energy out of nowhere (although energy doesn't have to be conserved if time itself gets messed up).

never took courses but why
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    Are you essentially asking "why should gravity be quantized?" – fqq Dec 12 '19 at 16:28
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    Also https://physics.stackexchange.com/q/52211/ https://physics.stackexchange.com/q/10088/ – fqq Dec 12 '19 at 16:29
  • @fqq: quantized gravity does not necessarily leads to graviton. For example, quantum gravity in $2+1$ dimensions does not have gravitons. – A.V.S. Dec 12 '19 at 16:34
  • @A.V.S. I was asking clarifications (and I misread the title). Anyway, that has been covered too. https://physics.stackexchange.com/q/102794/ – fqq Dec 12 '19 at 16:36
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    The phrase “Standard Model” has a specific meaning. There is no gravity and no graviton in the Standard Model. It is a model of the other three fundamental forces. – G. Smith Dec 12 '19 at 17:11
  • I'm glad I got an answer in before it was closed. I would add the comment of G. Smith to it. the SM does not have gravity. –  Dec 12 '19 at 18:21
  • @ggcg There are several possible duplicates of this on the site, perhaps you could recycle your answer on the better asked ones? – fqq Dec 13 '19 at 23:22

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I think you are mixing up several related things. A more basic question is why do we need a quantum theory of gravity in the first place! This is where the idea of the graviton comes from. Historically there have been many attempts to "unify" gravity with the other forces. And it is this desire that leads down the path of putting gravity in the standard model. However this has been difficult. Here are some of the paradigms that have shifted in and out of popularity, or really attempts to bring gravity and the other forces together.

  1. In the early days of Einstein's dream the electromagnetic force was sort of unified with gravity in the GR paradigm by adding extra dimensions. This was Kaluza-Klein theory. We were able to get a model of EM using components of the metric tensor in extra dimensions. In this paradigm EM would be space-time curvature just like gravity. There are problems with this approach that you can look up on your own.

  2. The SM is built by applying local symmetry to the "free" particle Lagrangian with a known global symmetry group. So a charged spinor particle Lagrangian has a global U(1) symmetry and locally gauging that gives us the EM field. Modern attempts to unify gravity with the other forces start with this mathematical paradigm. Particle physicists and QFT theorists see this approach as a starting point for any theory (doesn't mean they are right but they are very successful!). Once the classical Lagrangian is built that obeys all symmetries it is quantized and the states of the "particles", i.e. quanta of the field, derive their spin value from the space-time transformation properties of the field tensor. EM, W, and QCD are all space-time vectors, hence spin = 1, matter is described by spinors, spin = 1/2, Gravity is described by a second rank tensor, hence the expectation of a spin = 2 quanta. However! this assumes that the classical description of GR survives quantization and it may not.

  3. Problems with this effort have lead theorists to consider the possibility that (1) we cannot unify all forces so stop trying and (2) that perhaps gravity is a macro effect produced by the other forces in the SM. The latter idea was popular for a while in the 80s or 90s. Just get rid of GR at a fundamental level and see if one can build up a description of this field by average over states of all the other fields. This idea has failed.

  4. Richard Feynman tried to quantize GR by considering the equations of GR to be as they are given but without the interpretation of a curved space time. He assumed, like any good particle or QFT theorist, that space-time was fundamentally Lorentzian and that the linearized equations of GR (those that describe G-waves) were like any other field that could be quantized. This was done by applying perturbation theory to the full non-linear equations like we do with every other field, a process developed in large part of Feynman. He spent about 10 years on it and it did not work. This is published in Feynman's Lectures on Gravity.

  5. Progress was made using new variables by Abhay Ashtekar and I think is the foundation of loop quantum gravity.

  6. String theory completely changes the paradigm of everything by assuming strings or membranes vibrating freely in an N-dim space-time. From what I recall the structure of the EM and GR both emerge down stream after some calculations and manipulations of the full string Lagrangian.

Some of these paradigms do NOT assume a priori that gravity is the curvature of space-time and hence "not a force". And as you can see attempts have been made to make the other fields part of space-time curvature and hence "not and force". So in some sense it isn't fair to say Gravity can't have spin because it isn't a force when this statement mixes two different paradigms. As we learn more we may find that one or more of the basic elements of modern physics needs to be abandoned. For example, if gravity as we know it is a macro effect in the large N limit of some other theory it may be that the true quanta are not spin = 2 but that several quanta combine into a larger state function that behaves like a metric tensor. And, as I think I said, it may be that GR is correct and simply cannot be quantized. It may be that nature abhors unification!