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 nonstandard scalar kinetic Lagrangian that manifests itself through the inflationary sound speed c(s)(2). We extend the analytical approximations exploited in Contaldi et al. [J. Cosmol. Astropart. Phys. 07 (2003) 002] and Thavanesan et al. [Phys. Rev. D 103, 023519 (2021)] 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 wave number 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 in the early universe results in nondecaying oscillations in the resultant power spectra for the comoving curvature perturbation.