You are correct that in the framework of general relativity, gravity is described as the curvature of spacetime rather than a force in the traditional sense. However, the search for a theory of quantum gravity or the existence of a particle called the graviton is motivated by the desire to understand how gravity behaves at the quantum level.
In the realm of quantum mechanics, all other fundamental forces (electromagnetic, strong nuclear, and weak nuclear forces) are described by quantum field theories, which involve the exchange of particles known as force carriers or gauge bosons. For example, the electromagnetic force is mediated by photons, and the strong force is mediated by gluons.
The quest for a theory of quantum gravity arises from the desire to reconcile the principles of quantum mechanics with the framework of general relativity. The goal is to understand how gravity can be consistently described at the quantum level and how it interacts with other fundamental forces.
The hypothetical particle called the graviton is postulated in certain theoretical frameworks as the force carrier of gravity in a quantum theory of gravity. Just as photons mediate the electromagnetic force, the graviton would mediate the gravitational force at the quantum level. However, it is important to note that the existence and properties of the graviton are still purely speculative and have not been experimentally confirmed.
The search for a theory of quantum gravity and the graviton is driven by the desire to achieve a more complete and unified understanding of the fundamental forces of nature. Such a theory would help explain phenomena that occur in extreme gravitational conditions, such as the early moments of the universe, the behavior of black holes, and the nature of singularities. It would also potentially provide insights into the nature of spacetime itself and the fundamental structure of the universe.