Is gravity a fundamental force or a curvature of space-time?

There are basically two schools of thought about gravity, one I shall call the curvature or Einstein model, and the other one I shall call the particle model.

The Einstein model asserts that gravity is a curvature of spacetime and is the one predominately thought in schools, mainly because the particle model is more difficult to explain.

The particle model on the other hand asserts that, just like the other forces of nature, the force of gravity is transmitted via a virtual spin-2 particle called the graviton. The particle model also says that the graviton affects, or couples to, each other particle including other gravitons.

The predictions these models make are the same, because gravitons couple to everything, and to themselves, they can certainly give the same appearance as a theory of bent spacetime because there is no way to distinguish it (because there is nothing that does not couple to the graviton, and thus gravity) from a model with a rigid spacetime but with graviton self-interaction.

In fact using the framework of quantum field theory, one can show that one arises at exactly the same equations using the particle model as when using the curvature model.

The curvature model is older, being the model Einstein used himself, but the particle model seems to put gravity on equal footing as the other three fundamental forces (electromagnetism, weak and strong forces) which is also very pleasing. The particle model, however, has not yet been successfully been merged with the other three forces due to internal inconsistencies.

We have not yet seen a graviton in a particle collider because gravity is extremely weak compared to the other forces (consider a simple magnet able to lift up a piece of iron even with the entire gravity of the Earth pulling on it!) so a graviton would only couple very weakly so it would be very hard to detect. In fact I can probably not overstate how hard it would be.

A graviton couples so weakly that its influence would only become important in particle interactions at very high energies, and it is likely that at that point new physics will also emerge, such as the possible discreteness of space and time for example.