The Hypothesis is that the Graviton could be the force carrier for gravity. But with the knowledge of Einsteins theory of relativity which states that Gravity is NOT a Force, wouldn’t the Graviton disprove Relativity or at least some aspects of it?
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General relativity did not “disprove” Newtonian mechanics. It extended the range of scenarios where you can apply it and get valid answers. In certain specific scenarios, (e.g. throwing a ball into the air) Newtonian mechanics works really well. Relativity “simplifies” to Newtonian mechanics in those scenarios.
Similarly, a theory of quantum gravity wouldn’t “disprove” relativity, but it would allow us to compute accurate predictions in situations where we know classical relativity doesn’t apply, (e.g. in very hot or very dense scenarios like the fraction of a second just after the big bang). Such a theory would “simplify” to general relativity in situations where we currently know that relativity works well (e.g. for computing the orbits of planets). Part of the challenge of coming up with a good quantum gravity theory is getting it to “match” relativity in those mundane scenarios.
There are lots of reasons we expect a quantum theory of gravity. Here are a few I can immediately think of:
1) Singularity theorems. There are mathematical proofs that classical relativity breaks in certain scenarios. We need a way to avoid these.
3) Every other field is quantized. General relativity is something called a “classical field theory”. Every other time physicists have had a field like this which describes another type of interaction (i.e. electromagnetism, strong interaction, and weak interaction) we have been able to take the theory and “quantise it”. This quantized theory has worked really well. Why not do this for gravity?
4) There are [mathematical theorems](https://en.m.wikipedia.org/wiki/Weinberg%E2%80%93Witten_theorem) that show that you cannot make any quantum field theory where the graviton can be broken down into multiple “component particles” reduce to classical general relativity in those mundane situations I spoke about above. The graviton must be a fundamental particle, and no quantum theory could simplify to classical relativity without them.
5) Black hole thermodynamics. We can already “do quantum gravity” pretty well in under certain conditions (words to search here are things like “semiclassical gravity” and “effective field theory”). Using this, we can show that black holes have thermodynamic properties like temperature. Unfortunately, if you follow these ideas, you end up with certain difficulties relating to mathematical theories of information. One way to resolve these is with a full quantum theory of gravitons.
6) Holography and the AdS/CFT correspondence. It is pretty well understood that (at least under certain conditions) theories of gravitons can be rewritten as theories without gravitons. We understand quantum field theory very well when there are no gravitons. We can use this “correspondence” to understand things about quantized gravitons.
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