We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a single scalar field with a general kinetic term and a general form of the potential .
We employ the ADM formalism and the spatial gradient expansion approach , characterised by O ( \epsilon ^ { m } ) , where \epsilon = 1 / ( HL ) is a small parameter representing the ratio of the Hubble radius to the characteristic length scale L of perturbations .
We obtain the general solution for a full nonlinear version of the curvature perturbation valid up through second-order in \epsilon ( m = 2 ) .
We find the solution satisfies a nonlinear second-order differential equation as an extension of the equation for the linear curvature perturbation on the comoving hypersurface .
Then we formulate a general method to match a perturbative solution accurate to n -th-order in perturbation inside the horizon to our nonlinear solution accurate to second-order ( m = 2 ) in the gradient expansion on scales slightly greater than the Hubble radius .
The formalism developed in this paper allows us to calculate the superhorizon evolution of a primordial non-Gaussianity beyond the so-called \delta N formalism or separate universe approach which is equivalent to leading order ( m = 0 ) in the gradient expansion .
In particular , it can deal with the case when there is a temporary violation of slow-roll conditions .
As an application of our formalism , we consider Starobinsky ’ s model , which is a single field model having a temporary non-slow-roll stage due to a sharp change in the potential slope .
We find that a large non-Gaussianity can be generated even on superhorizon scales due to this temporary suspension of slow-roll inflation .