K-inflationary Power Spectra at Second Order
  Within the class of inflationary models, k-inflation represents the most
general single field framework that can be associated with an effective
quadratic action for the curvature perturbations and a varying speed of sound.
The incoming flow of high-precision cosmological data, such as those from the
Planck satellite and small scale Cosmic Microwave Background (CMB) experiments,
calls for greater accuracy in the inflationary predictions. In this work, we
calculate for the first time the next-to-next-to-leading order scalar and
tensor primordial power spectra in k-inflation needed in order to obtain robust
constraints on the inflationary theory. The method used is the uniform
approximation together with a second order expansion in the Hubble and sound
flow functions. Our result is checked in various limits in which it reduces to
already known situations.
