A scaling invariance of the perturbations in $k$-inflation models

TL;DR

This paper explores a scaling invariance property in $k$-inflation models, showing how it can be used to adjust parameters for correct CMB spectrum normalization, supported by numerical analysis of specific models.

Contribution

It reveals a general scaling property in $k$-essence inflation models and demonstrates its application to model normalization at the CMB scale.

Findings

Scaling invariance simplifies parameter redefinition in $k$-inflation models.

Numerical integration confirms the scaling property in specific models.

Perturbation spectra can be normalized correctly using the scaling property.

Abstract

We study the background and perturbations in $k$-essence inflation models and show that a general $k$-essence exhibits a simple scaling property. In particular, we study two classes of $k$-inflation models with the potential characterized by an inflection point. We demonstrate that these models enjoy scaling properties that could be used to redefine input parameters so that the perturbation spectra satisfy correct normalization at the CMB pivot scale. The background and perturbation equations are integrated numerically for two specific models.