Primordial power spectra from $k$-inflation with curvature

Understand

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 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.