We explicitly show the fully nonlinear equivalence of the $\delta \mathrm{N}$ and the covariant formalisms for the superhorizon curvature perturbations, which enables us to safely evaluate the non-Gaussian quantities of the curvature perturbation in either formalism. We also discuss isocurvature perturbations in the covariant formalism and clarify the relation between the fully nonlinear evolution of the curvature covector and that of the curvature perturbation for multiple interacting fluids.

• Received 29 January 2012

DOI:https://doi.org/10.1103/PhysRevD.85.083504