A note on perfect scalar fields

TL;DR

This paper characterizes perfect scalar fields by a condition on their Lagrangian, shows they reduce to pure kinetic models under redefinition, and demonstrates their inability to produce features in inflationary spectra.

Contribution

It introduces a condition for perfect scalar fields, relates them to pure kinetic models, and analyzes their implications for inflationary perturbations.

Findings

Perfect scalar fields have a specific Lagrangian condition.

Models that appear to depend on the scalar field can be redefined as pure kinetic.

Perfect scalar fields cannot generate features in the inflationary spectrum.

Abstract

We derive a condition on the Lagrangian density describing a generic, single, non-canonical scalar field, by demanding that the intrinsic, non-adiabatic pressure perturbation associated with the scalar field vanishes identically. Based on the analogy with perfect fluids, we refer to such fields as perfect scalar fields. It is common knowledge that models that depend only on the kinetic energy of the scalar field (often referred to as pure kinetic models) possess no non-adiabatic pressure perturbation. While we are able to construct models that seemingly depend on the scalar field and also do not contain any non-adiabatic pressure perturbation, we find that all such models that we construct allow a redefinition of the field under which they reduce to pure kinetic models. We show that, if a perfect scalar field drives inflation, then, in such situations, the first slow roll parameter will always be a monotonically decreasing function of time. We point out that this behavior implies that these scalar fields can not lead to features in the inflationary, scalar perturbation spectrum.