A note on second-order perturbations of non-canonical scalar fields

TL;DR

This paper investigates second-order perturbations of non-canonical scalar fields in cosmology, revealing potential instabilities at this order that are absent at linear order, and discusses conditions on the Lagrangian affecting these instabilities.

Contribution

It provides a detailed analysis of second-order perturbations for non-canonical scalar fields, highlighting potential instabilities and conditions on the Lagrangian, which were not previously well-characterized.

Findings

Second-order perturbations can exhibit instabilities not seen at linear order.

Conditions on the Lagrangian influence the presence of these instabilities.

Discussion on the linearization instability of non-canonical scalar fields.

Abstract

We study second-order perturbations for a general non-canonical scalar field, minimally coupled to gravity, on the unperturbed FRW background, where metric fluctuations are neglected a priori. By employing different approaches to cosmological perturbation theory, we show that, even in this simplified set-up, the second-order perturbations to the stress tensor, the energy density and the pressure display potential instabilities, which are not present at linear order. The conditions on the Lagrangian under which these instabilities take place are provided. We also discuss briefly the significance of our analysis in light of the possible linearization instability of these fields about the FRW background.