A general proof of the equivalence between the δN and covariant formalisms

Recently, the equivalence between the delta N and covariant formalisms has been shown by Suyama et al. but they essentially assumed Einstein gravity in their proof (arXiv:1201.3163). They showed that the evolution equation of the curvature covector in the covariant formalism on uniform energy density slicings coincides with that of the curvature perturbation in the dN formalism assuming the coincidence of uniform energy and uniform expansion (Hubble) slicings, which is the case on superhorizon scales in Einstein gravity. In this short note, we explicitly show the equivalence between the delta N and covariant formalisms without specifying the slicing condition and the associated slicing coincidence, in other words, regardless of the gravity theory. Copyright (C) EPLA, 2012