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Towards the goal to quantize gravity, in this short review we discuss anintermediate step which consists in extending the picture of standard GeneralRelativity by considering Extended Theories of Gravity. In this tapestry, theequations to quantize are not the standard Einstein field equations of GeneralRelativity, but the extended Einstein field equations of such ExtendedTheories. The traditional relation between mass-energy and space-timecurvature, which founds standard General Relativity, results modified in thisnew picture and, at least at the linearized approximation, variations of thespace-time curvature generate the mass-energy. Various problems of the DarkUniverse, Dark Energy, Dark Matter and Pioneer anomaly, can be, in principle,solved through this approach, while a definitive endorsement for ExtendedTheories of Gravity could arrive from the realization of a consistentgravitational wave astronomy. We also discuss the quantization of bothmass-energy and space-time curvature in the early Universe by using the processof amplification of vacuum fluctuations which is connected with the primordialproduction of relic gravitational waves. A future detection of such relicgravitational waves will be an ultimate endorsement for the quantum rather thanclassical feature of the gravitational interaction.

Dark Energy and Dark Matter like intrinsic curvature in extended gravity. Viability through gravitational waves