K-inflationary Power Spectra at Second Order

TL;DR

This paper computes second-order scalar and tensor primordial power spectra in k-inflation, enhancing the precision of inflationary predictions to match high-precision cosmological data.

Contribution

It introduces a novel second-order calculation of power spectra in k-inflation using the uniform approximation, improving accuracy for observational constraints.

Findings

First second-order power spectra for k-inflation derived

Results consistent with known limits and special cases

Provides tools for more precise inflationary model testing

Abstract

Within the class of inflationary models, k-inflation represents the most general single field framework that can be associated with an effective quadratic action for the curvature perturbations and a varying speed of sound. The incoming flow of high-precision cosmological data, such as those from the Planck satellite and small scale Cosmic Microwave Background (CMB) experiments, calls for greater accuracy in the inflationary predictions. In this work, we calculate for the first time the next-to-next-to-leading order scalar and tensor primordial power spectra in k-inflation needed in order to obtain robust constraints on the inflationary theory. The method used is the uniform approximation together with a second order expansion in the Hubble and sound flow functions. Our result is checked in various limits in which it reduces to already known situations.