Probing the dark Universe with gravitational waves

Gravitational waves (GW) are expected to interact with dark energy and dark matter, affecting their propagation on cosmological scales. In order to model this interaction, we derive a gauge invariant effective equation and action valid for all GWs polarizations, based on encoding the effects of the interaction of GWs at different order in perturbations, in a polarization, frequency and time dependent effective speed. The invariance of perturbations under time dependent conformal transformations and the gauge invariance of the GWs allow to obtain the unitary gauge effective action in any conformally related frame, making transparent the relation between Einstein and Jordan frame. The propagation time and luminosity distance of different GWs polarizations allow to probe at different frequencies and redshift the dark Universe, which act as an effective medium, whose physical properties can be modeled by the GWs effective speed.