Nonlinear superhorizon curvature perturbation in generic single-field inflation

We develop a theory of nonlinear cosmological perturbations on superhorizon scales for generic single-field inflation. Our inflaton is described by the Lagrangian of the form $W(X,ϕ)-G(X,ϕ)\Boxϕ$ with $X=-\partial^μϕ\partial_μϕ/2$, which is no longer equivalent to a perfect fluid. This model is more general than k-inflation, and is called G-inflation. A general nonlinear solution for the metric and the scalar field is obtained at second order in gradient expansion. We derive a simple master equation governing the large-scale evolution of the nonlinear curvature perturbation. It turns out that the nonlinear evolution equation is deduced as a straightforward extension of the corresponding linear equation for the curvature perturbation on uniform $ϕ$ hypersurfaces.

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