The evolution of gravitons in accelerating cosmologies: the case of extended gravity

We discuss the production and evolution of cosmological gravitons showing how the cosmological background affects their dynamics. Besides, the detection of cosmological gravitons could constitute an extremely important signature to discriminate among different cosmological models. Here we consider the cases of scalar-tensor gravity and $f(R)$ gravity where it is demonstrated the amplification of graviton amplitude changes if compared with General Relativity. Possible observational constraints are discussed.