Why can the graviton not be a spin 0 particle? On a similar note why can it not be a spin 4, spin 6 particle?
Answer
For force carriers the interacting field theory determines the spin. A scalar field yields spin 0; the Higgs is the only example; a vector field yields spin 1, the photon, W, and Z are examples; a tensor field yields spin 2.
Since gravitational field theory requires a tensor field for General Relativity, quantized gravity, in the weak-field, linearized limit, yields the spin 2 graviton.
Higher order spins can be constructed from complex particles, meaning systems with two or more constituents.
For more information see Would a spin-2 particle necessarily have to be a graviton?
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