Each of the carriers were predicted by the (then new) study of “quantum field theory”, and have since been observed. So, some physicists are looking for evidence of the existence of gravitons (the gravity particle), because it would really tie things together nicely. Gravity is a really, really weak force, and a graviton is the smallest amount of that force that can exist. Most physicists have already given up any hope of detecting the graviton directly, and instead are looking at extremely indirect methods. To actually answer the question: some physicists are looking for the graviton because it “fits”.