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The effective field theory (EFT) of inflation provides an essential pictureto explore the effects of the unknown high energy physics in the single scalarfield inflation models. For a generic EFT of inflation, possible high energycorrections to simple slow-roll inflation can modify both the propagating speedand dispersion relations of the cosmological scalar and tensor perturbations.With the arrival of the era of precision cosmology, it is expected that thesehigh energy corrections become more important and have to be taken into accountin the analysis with future precise observational data. In this paper we studythe observational predictions of the EFT of inflation by using the third-orderuniform asymptotic approximation method. We calculate explicitly the primordialpower spectra, spectral indices, running of the spectral indices for bothscalar and tensor perturbations, and the ratio between tensor and scalarspectra. These expressions are all written in terms of the Hubble flowparameters and the flow of four new slow-roll parameters and expanded up to thenext-to-leading order in the slow-roll expansions so they represent the mostaccurate results obtained so far in the literature. The flow of the four newslow-roll parameters, which arise from the four new operators introduced in theaction of the EFT of inflation, can affect the primordial perturbation spectraat the leading-order and the corresponding spectral indices at thenext-to-leading order.

Inflationary perturbation spectra at next-to-leading slow-roll order in effective field theory of inflation