Gauge-invariant perturbations at second order: multiple scalar fields on large scales

We derive the governing equations for multiple scalar fields minimally coupled to gravity in a flat Friedmann-Robertson-Walker background spacetime on large scales. We include scalar perturbations up to second order and write the equations in terms of physically transparent gauge-invariant variables at first and second order. This allows us to write the perturbed Klein-Gordon equation at second order solely in terms of the field fluctuations on flat slices at first and second order.