Is the Effective Field Theory of Dark Energy Effective?

Abstract: The effective field theory of cosmic acceleration systematizes possible contributions to the action, accounting for both dark energy and modifications of gravity. Rather than making model dependent assumptions, it includes all terms, subject to the required symmetries, with four (seven) functions of time for the coefficients. These correspond respectively to the Horndeski and general beyond Horndeski class of theories. We address the question of whether this general systematization is actually effective, i.e. useful in revealing the nature of cosmic acceleration when compared with cosmological data. The answer is no and yes: {\it there is no simple time dependence of the free functions} -- assumed forms in the literature are poor fits, but one can derive some general characteristics in early and late time limits. For example, we prove that the gravitational slip must restore to general relativity in the de Sitter limit of Horndeski theories, and why it doesn't more generally. We also clarify the relation between the tensor and scalar sectors, and its important relation to observations; in a real sense the expansion history $H(z)$ or dark energy equation of state $w(z)$ is $1/5$ or less of the functional information! In addition we discuss the de Sitter, Horndeski, and decoupling limits of the theory utilizing Goldstone techniques.