is graviton does really exist?
Not currently known, there is no experimental support for the graviton at this time. On the other hand, General Relativity (which does not postulate gravitons) is a successful theory.
A better question would be why would a graviton particle theory be accepted. There is no direct evidence for gravitational waves, much less gravitons, so why would their existence be accepted?
Well, since Quantum Field Theories were really effiecient in describing the other 3 interactions, people hope it can be used for gravitation as well, that's why graviton is hoped to exist.
Postulating the existence of such a particle will also give Newton's 1/r law in the classical limit(just like GR), which is a good thing, but... There are problems with incorporating gravitons to the Standard Model of praticle physics, so this is kind of one frontier of theoretical(and mathematical) physics...
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