A short note on the curvature perturbation at second order
  Working with perturbations about an FLRW spacetime, we compute the
gauge-invariant curvature perturbation to second order solely in terms of
scalar field fluctuations. Using the curvature perturbation on uniform density
hypersurfaces as our starting point, we give our results in terms of field
fluctuations in the flat gauge, incorporating both large and small scale
behaviour. For ease of future numerical implementation we give our result in
terms of the scalar field fluctuations and their time derivatives.
