Motions of the planets put new limit on graviton mass. Range of gravitational field cannot be shorter than 18 trillion kilometreshttps://physicsworld.com/a/motions-of-the-planets-put-new-limit-on-graviton-mass/ …
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Or a fine tuned nonabelian gauge theory
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Have the temptation to say: the s=2 graviton acquires a little mass not due to Higgs but due to a small "self interaction" (3, 4 vertices) implying a non-abelian or "almost abelian" structure of the theory. In fact gravity can be formulated as a non abelian gauge SL(2,C) theory.
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Even (IR) weakly coupled nonabelian theories have coulomb-like potentials at low-energy, afaik
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