Primordial power spectra from $k$-inflation with curvature

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.

12 pages, 5 figures; v1: As submitted to PRD. v2: As published in PRD

References in corpus (11)

• In the Realm of the Hubble tension $-$ a Review of Solutions
• Planck evidence for a closed Universe and a possible crisis for cosmology
• anesthetic: nested sampling visualisation
• Just enough inflation: power spectrum modifications at large scales
• CMB quadrupole suppression: I. Initial conditions of inflationary perturbations
• CMB quadrupole suppression: II. The early fast roll stage
• A note on perfect scalar fields
• Analytical approximations for curved primordial power spectra
• Constraining Quantum Initial Conditions before Inflation
• Logolinear series expansions with applications to primordial cosmology
• Spatial Curvature at the Sound Horizon

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• Reconstructing square-law k-inflation from Planck data