Power spectra and spectral indices of $k$-inflation: high-order corrections

Understand

$k$-inflation represents the most general single-field inflation, in which the perturbations usually obey an equation of motion with a time-dependent sound speed.

• In this paper, we study the observational predictions of the $k$-inflation by using the high-order uniform asymptotic approximation method.
• We calculate explicitly the slow-roll expressions of the power spectra, spectral indices, and running of the spectral indices for both the scalar and tensor perturbations.
• These expressions are all written in terms of the Hubble and sound speed flow parameters.