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.