Physical Review D9-119 VanDam et al. You could try searching through Article indexes of Nature, Scientific American, and Physics Today since they have articles which you could be understand but would have plenty of information on why the graviton should exist. Basically, Einstein's theory of gravity says that gravity is not really a force but space-time is really curved around high mass objects like stars or better black holes. So particles around these feel like they are on a steep hill and roll inward towards it. The deviation from regular old Newtonian gravity is small but it is observable.
String theory is an exception but is based on completely different paradigms.
If you do try to make a quantum theory of gravity though, the graviton pops out as the force carrier. Published in Phys. These are published in journals which are widely read at universities but you won't find them at the local library. They usually explain things well and touch on a variety of subjects. Anyway, good luck.