Of the Four Forces…Gravity, Electromagnetizm, Weak and Strong Nuclear Forces…only 3 are described by the Standard Model. Gravity alone must have it’s own unique theory.
Einstein always believed that what we perceive as a force was merely a distortion of spacetime.
Suppose we take that advice literally.
If we stop attempting to quantize gravity as a function of matter or energy like a force particle and instead quantize spacetime at the Planck Scale…as Loop Quantum Gravity seems to do…would the resulting quantized spacetime manifest as “particles”?
No one knows. What we do know is that if there is such a thing as a graviton that follows quantum mechanical rules, it would have to have specific properties so as to not directly contradict the observed behavior of gravity. It would have to be massless, electrically neutral and have a spin value of 2.
Without a working quantum theory of gravity, we can’t say anything for certain. And we certainly can’t say how gravitons would behave (at least, not in the same sort of detail that we can say for photons). But it would be exceedingly weird if they don’t exist, and I don’t think that there are any serious models which reject their existence.