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We provide a compact and unified treatment of power spectrum observables forthe effective field theory (EFT) of inflation with the complete set ofoperators that lead to second-order equations of motion in metric perturbationsin both space and time derivatives, including Horndeski and GLPV theories. Werelate the EFT operators in ADM form to the four additional free functions oftime in the scalar and tensor equations. Using the generalized slow rollformalism, we show that each power spectrum can be described by an integralover a single source that is a function of its respective sound horizon. Withthis correspondence, existing model independent constraints on the sourcefunction can be simply reinterpreted in the more general inflationary context.By expanding these sources around an optimized freeze-out epoch, we alsoprovide characterizations of these spectra in terms of five slow-rollhierarchies whose leading order forms are compact and accurate as long as EFTcoefficients vary only on timescales greater than an efold. We also clarify therelationship between the unitary gauge observables employed in the EFT and thecomoving gauge observables of the post-inflationary universe.

Generalized Slow Roll in the Unified Effective Field Theory of Inflation