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