标题： δN形式主义之外 显示英文标题

标题： Beyond δN formalism

摘要： 我们发展了一种在暴胀宇宙学背景下，具有广义动能项和势能形式的多组分标量场在超视界尺度上的非线性宇宙扰动理论。 我们采用ADM形式和空间梯度展开方法，其特征为O(\epsilon ^2)，其中\epsilon=1 /(HL) 是一个表示扰动特征长度尺度 L 与哈勃半径之比的小参数。 我们提供了一个用于获得多场情况下的解的形式框架。 该框架可以应用于超出所谓的\delta N 形式之外的原初非高斯性的超视界演化，该形式等价于梯度展开中的 O(\epsilon ^0)。 在此过程中，我们还推导了适用于 O(\epsilon ^2) 的完全非线性坐标变换规则。 这些完全非线性的坐标变换规则可用于从计算更为简单的坐标中的解中推导出所需坐标中的解。 作为演示，我们考虑了一个可解析求解的模型，并显式地构造了解。 显示英文摘要

摘要： 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.