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

为了估计原初非高斯性，非线性宇宙学微扰理论是非常重要的。超视界尺度上的宇宙学扰动在所谓的分离宇宙方法或δ N-形式主义中得到了广泛的研究。由于曲率扰动的演化可以用背景量来描述，且计算简单，因此它们是估计非高斯性的有力工具。然而，在这方面，它们的形式本质上是空间梯度展开的首阶近似，以前的许多研究都局限于此.我们发展了一种非线性超视界微扰理论，得到了具有非正则动力学项和一般势的单个标量场的梯度展开的次首阶通解，并发现该解满足非线性第二阶近似.作为同动超曲面上线性曲率扰动方程的自然推广，得到了一个新的二阶微分方程。

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.