Gauge invariant formulation of metric f (R) gravity for gravitational waves

We analyze the propagation of gravitational waves in metric f(R) theories of gravity, on the special setting of flat background geometry (Minkowski spacetime). In particular, adopting a gauge invariant formalism, we clearly establish that the exact number of propagating degrees of freedom is three, consisting of the standard tensorial modes along with an additional massive scalar field. Then, investigating their effects on test masses via the geodesic deviation equation, we show that the additional dynamical degree contained in such extended formulations is actually detectable as a superposition of longitudinal and breathing stresses, which even though in principle correspond to distinct pure polarizations turn out to be never separable in the wave dynamics and cannot be interpreted as a proper independent excitations.