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