Nonperturbative δN formalism

We revisit the question of how to calculate correlations of the curvature perturbation, zeta, using the delta N formalism when one cannot employ a truncated Taylor expansion of N. This problem arises when one uses lattice simulations to probe the effects of isocurvature modes on models of reheating. Working in real space, we use an expansion in the cross-correlation between fields at different positions and present simple expressions for observables such as the power spectrum and the reduced bispectrum, f(NL). These take the same form as those of the usual delta N expressions, but with the derivatives of N replaced by nonperturbative delta N coefficients. We test the validity of this expansion and, when compared to others in the literature, argue that our expressions are particularly well suited for use with simulations.