We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a multi-component scalar field with a general kinetic term and a general form of the potential in the context of inflationary cosmology .
We employ the ADM formalism and the spatial gradient expansion approach , characterised by { \cal O } ( \epsilon ^ { 2 } ) , where \epsilon = 1 / ( HL ) is a small parameter representing the ratio of the Hubble radius to the characteristic length scale L of perturbations .
We provide a formalism to obtain the solution in the multi-field case .
This formalism can be applied to the superhorizon evolution of a primordial non-Gaussianity beyond the so-called \delta N formalism which is equivalent to { \cal O } ( \epsilon ^ { 0 } ) of the gradient expansion .
In doing so , we also derive fully nonlinear gauge transformation rules valid through { \cal O } ( \epsilon ^ { 2 } ) .
These fully nonlinear gauge transformation rules can be used to derive the solution in a desired gauge from the one in a gauge where computations are much simpler .
As a demonstration , we consider an analytically solvable model and construct the solution explicitly .