  We derive an effective equation and action for comoving curvature
perturbations and gravitational waves (GWs) in terms of a time, momentum and
polarization dependent effective speed, encoding the effects of the interaction
among metric perturbations or with other fields, such as dark energy and dark
matter. The structure of the effective actions and equations is the same for
scalar and tensor perturbations, and the effective actions can be written as
the Klein-Gordon action in terms of an appropriately defined effective metric,
dependent on the effective speed. The effective action reproduces, and
generalizes to higher order in perturbations, results obtained for GWs in the
effective field theory of inflation and dark energy, or for curvature
perturbations in systems with multiple scalar fields, encoding in the effective
speed the effects of both entropy and anisotropy. The effective approach can
also be applied to the solutions of theories with field equations different
from the Einstein equations, by defining an appropriate effective
energy-momentum tensor. As an example, we show that for a minimally coupled
scalar field in general relativity, the effective speeds of curvature
perturbations and gravitational waves are frequency and polarization dependent,
due to their coupling in the action beyond the quadratic order.
