Primordial power spectra from k-inflation with curvature
  We investigate the primordial power spectra for general kinetic inflation
models that support a period of kinetic dominance in the case of curved
universes. We present derivations of the Mukhanov-Sasaki equations with a
non-standard scalar kinetic Lagrangian which manifests itself through the
inflationary sound speed $c_s^2$. We extend the analytical approximations
exploited in Contaldi et al [1] and Thavanesan et al [2] to general kinetic
Lagrangians and show the effect of k-inflation on the primordial power spectra
for models with curvature. In particular, the interplay between sound speed and
curvature results in a natural low wavenumber cutoff for the power spectra in
the case of closed universes. Using the analytical approximation, we further
show that a change in the inflationary sound speed between different epochs of
inflation results in non-decaying oscillations in the resultant power spectra
for the comoving curvature perturbation.
