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Over the last few years, it was realised that non-canonical scalar fields canlead to the accelerated expansion in the early universe. The primordialspectrum in these scenarios not only shows near scale-invariance consistentwith CMB observations,but also large primordial non-Gaussianity. Second-orderperturbation theory is the primary theoretical tool to investigate suchnon-Gaussianity. However, it is still uncertain which quantities aregauge-invariant at second-order and their physical understanding thereforeremains unclear. As an attempt to understand second order quantities, weconsider a general non-canonical scalar field, minimally coupled to gravity, onthe unperturbed FRW background where metric fluctuations are neglected apriori. In this simplified set-up, we show that there arise ambiguities in theexpressions of physically relevant quantities, such as the effective speeds ofthe perturbations. Further, the stress tensor and energy density display apotential instability which is not present at linear order.

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