  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.
