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 $W(X,\varphi )-G(X,\varphi )\mathrm{\square }\varphi$ with $X=-{\mathrm{\partial }}^{\mu }\varphi {\mathrm{\partial }}_{\mu }\varphi \mathrm{/}2$, 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 $\varphi$ hypersurfaces.