Perturbations in k-inflation

TL;DR

This paper generalizes cosmological perturbation theory to include k-inflation models with non-minimal kinetic terms, providing a framework to distinguish these models observationally from standard inflation.

Contribution

It extends the theory of cosmological perturbations to arbitrary scalar field Lagrangians, including k-inflation, and calculates the resulting fluctuation spectra.

Findings

Derived the spectrum of quantum fluctuations for k-inflation.

Showed the modification of the consistency relation between tensor and scalar perturbations.

Demonstrated that k-inflation can be phenomenologically distinguished from standard inflation.

Abstract

We extend the theory of cosmological perturbations to the case when the ``matter'' Lagrangian is an arbitrary function of the scalar field and its first derivatives. In particular, this extension provides a unified description of known cases such as the usual scalar field and the hydrodynamical perfect fluid. In addition, it applies to the recently proposed k-inflation, which is driven by non-minimal kinetic terms in the Lagrangian. The spectrum of quantum fluctuations for slow-roll and power law k-inflation is calculated. We find, for instance, that the usual ``consistency relation'' between the tensor spectral index and the relative amplitude of scalar and tensor perturbations is modified. Thus, at least in principle, k-inflation is phenomenologically distinguishable from standard inflation.