  We study the second-order gauge-invariant adiabatic and isocurvature
perturbations in terms of the scalar fields present during inflation, along
with the related fully non-linear space gradient of these quantities. We
discuss the relation with other perturbation quantities defined in the
literature. We also construct the exact cubic action of the second-order
perturbations (beyond any slow-roll or super-horizon approximations and
including tensor perturbations), both in the uniform energy density gauge and
the flat gauge in order to settle various gauge-related issues. We thus provide
the tool to calculate the exact non-Gaussianity beyond slow-roll and at any
scale.
