Ambiguities in second-order cosmological perturbations for non-canonical scalar fields

TL;DR

This paper investigates second-order perturbations in non-canonical scalar fields, revealing gauge ambiguities and potential instabilities that impact understanding of early universe acceleration and primordial non-Gaussianity.

Contribution

It highlights ambiguities in gauge-invariant quantities at second-order and uncovers potential instabilities in stress tensor and energy density for non-canonical scalar fields.

Findings

Ambiguities in gauge-invariant second-order quantities.

Potential instabilities in stress tensor and energy density.

Effective speeds of perturbations are not uniquely defined.

Abstract

Over the last few years, it was realised that non-canonical scalar fields can lead to the accelerated expansion in the early universe. The primordial spectrum in these scenarios not only shows near scale-invariance consistent with CMB observations,but also large primordial non-Gaussianity. Second-order perturbation theory is the primary theoretical tool to investigate such non-Gaussianity. However, it is still uncertain which quantities are gauge-invariant at second-order and their physical understanding therefore remains unclear. As an attempt to understand second order quantities, we consider a general non-canonical scalar field, minimally coupled to gravity, on the unperturbed FRW background where metric fluctuations are neglected a priori. In this simplified set-up, we show that there arise ambiguities in the expressions of physically relevant quantities, such as the effective speeds of the perturbations. Further, the stress tensor and energy density display a potential instability which is not present at linear order.