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