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An effective model independent approach for the study of gravitational waves(GW) propagation is derived with two different methods, one based on theeffective stress-energy-momentum tensor (EST), and the other on the effectiveaction, generalizing the effective field theory (EFT) of dark energy to systemswith an arbitrary matter Lagrangian. The effective action is derived inEinstein and Jordan frame, and it depends on an effective GW speed and aneffective Planck mass, which can both depend on time, frequency, andpolarization, due to the effects of higher order interaction terms. The GWpropagation friction term can be polarization and frequency dependent, inducinga time, frequency and polarization dependent ratio between GW andelectromagnetic luminosity distance. For theories with matter coupled to theEinstein frame metric the ratio depends on the effective speed, while forJordan frame matter coupling the ratio depends on the effective Planck mass.

The effects of dark energy on the propagation of gravitational waves