Study of non-Gaussianity of primordial density perturbations and theoretical models in the early universe

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In order to estimate the primordial non-Gaussianity, nonlinear cosmological perturbation theory is so important. Cosmological perturbations on superhorizon scales have been studied extensively in the so-called separate universe approach or delta N-formalism. Their approaches are powerful tool to estimate non-Gaussianity since the evolution of curvature perturbation can be described only by background quantities and it is easy to calculate. However, their formalism are essentially the leading-order approximation to the spatial gradient expansion and many of the previous studies were confined to it. We have developed a theory of nonlinear superhorizon perturbations and obtained a general solution valid up to the next-leading order in the gradient expansion for a single scalar field with non-canonical kinetic terms anda general potential and found the solution satisfies a nonlinear second-order differential equation as a natural extension of the equation for the linear curvature perturbation on the comoving hypersurface.