I'm trying to understand to what extent it is a "miracle" that a massless spin-2 field "postdicts" general relativity. I think there is some early theorem of Weinberg that shows under various assumptions and consistency requirements that spin-2 can't like be a Yang–Mills type theory, it has to couple in a gravity-like way, but I'm trying to understand exactly what this means. Are these arguments just for perturbations around flat spacetime, i.e. we don't know at all if they would describe observational classical general relativity around e.g. stars? To what extent do we really know that a massless spin-2 particle uniquely postdicts general relativity. For example, if general relativity hadn't yet been discovered, would the study of QFT lead people to come up with the exact Einstein equation for macroscopic matter as an inevitable consequence of any massless spin-2 QFT?
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$\begingroup$ Concerning the title question, what are you calling the "linearized limit"? Is it only the quadratic Fierz-Pauli part of the action (in the perturbation), or the full expansion of the EH action in terms of the perturbation? For the latter, and according to Deser arxiv.org/abs/gr-qc/0411023 after eq(1), it is a matter of imposing recursively some properties to the Fierz-Pauli equation of motion when there are interactions. $\endgroup$– Jeanbaptiste RouxCommented Dec 9, 2023 at 8:05
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$\begingroup$ I mean does massless spin 2 imply: a) weak field limit, b) classical strong field limit (but not UV), whereas I assume c) high energy / small distance would require a fuller quantum theory of gravity. $\endgroup$– user1247Commented Dec 9, 2023 at 14:51
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$\begingroup$ You meant to ask "can we device a spin-2 QFT that can accommodate general relativity" this imply existence of a spin-2 massless particle which can mediate gravity at all scale. I don't know the answer but interested in knowing it $\endgroup$– Aman pawarCommented May 11 at 23:28
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