The curvature perturbation at second order
  We give an explicit relation, up to second-order terms, between scalar-field fluctuations defined on spatially-flat slices and the curvature perturbation on uniform-density slices. This expression is a necessary ingredient for calculating observable quantities at second-order and beyond in multiple-field inflation. We show that traditional cosmological perturbation theory and the `separate universe' approach yield equivalent expressions for superhorizon wavenumbers, and in particular that all nonlocal terms can be eliminated from the perturbation-theory expressions. 
Mafalda Dias, Joseph Elliston, Jonathan Frazer, David Mulryne and   David Seery
gr-qc astro-ph.CO hep-th