Is the Graviton the Key to Understanding Gravity?

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Why?

As I understand it General Relativity states that gravity is the warping of space-time, so it seems a reasonable assumption that as a consequence of this that gravity does not require a force carrying particle as the strong and electroweak forces do. Are there theories being explored that follow this line of thought or am I totally off here?
 
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The graviton can be seen as a quantization applicable to "weak gravity", i.e. in the perturbative limit of small gravitational waves on a fixed metric background. It is by no means clerar whether this approach shall be applicable to gravity as a whole; there are clearly indications that this is the wrong way to go.

There are non-pertutrbaite approaches to quantum gravity, e.g. the asymptotoc safety program and loop quantum gravity. Asymptotic safety usually woks in the metric formalism, whereas as loop quantum gravity (spin networks, spin foams) starts with Ashtekar variables which are related to the first order formalism with connection representation. In both approaches there is nothing like a graviton as a building block of the quantum theory.

On the other hand there are approaches which seem to allow for a perturbative expansion based on gravitons, like supergravity (as a low-energy limit of string theory or as a fundamental theory), but even in these theories it's obvious that there is a non-perturbative sector where gravitons are of little relevance.
 
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