Beyond \delta N formalism

TL;DR

This paper develops a comprehensive nonlinear perturbation theory for multi-component scalar fields during inflation, extending the ta N formalism to include higher-order gradient effects and gauge transformations.

Contribution

It introduces a formalism for superhorizon evolution of nonlinear perturbations beyond ta N, including gauge transformation rules up to second order in gradient expansion.

Findings

Derived fully nonlinear gauge transformation rules valid through O(psilon^2)

Constructed explicit solutions in an analytically solvable model

Extended the ta N formalism to include multi-field and higher-order effects

Abstract

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 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 O(\epsilon^0) of the gradient expansion. In doing so, we also derive fully nonlinear gauge transformation rules valid through 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.