Primordial power spectra from $k$-inflation with curvature

TL;DR

This paper analyzes how general kinetic inflation models with curvature influence primordial power spectra, highlighting the effects of sound speed and curvature, including a low wavenumber cutoff and oscillations.

Contribution

It extends analytical approximations to general kinetic Lagrangians in curved universes, revealing new effects of sound speed and curvature on power spectra.

Findings

Curved universes induce a low wavenumber cutoff in power spectra.

Changes in sound speed cause non-decaying oscillations in the spectra.

Analytical methods are extended to general kinetic inflation models.

Abstract

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. 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.