arXiv 1004.18702010-04-12astro-ph.COgr-qchep-th

$δ$ N形式之外超视界曲率扰动的非高斯性

Non-Gaussianity of superhorizon curvature perturbations beyond $δ$ N formalism

Yu-ichi Takamizu, Shinji Mukohyama, Misao Sasaki, Yoshiharu Tanaka

备注：: 27 pages, 3 figures
发表信息：: JCAP 1006:019,2010
DOI：: 10.1088/1475-7516/2010/06/019

摘要：

本文对具有一般动力学项和一般势形式的单标量场发展了超视界尺度上的非线性宇宙学扰动理论。我们采用ADM形式主义和空间梯度展开的方法，其特征在于$O(ε^m)$，其中$ε=1/(HL)$是一个小参数，表示哈勃半径的比值的特征长度尺度$L$的扰动。我们得到了一个完整的非线性版本的曲率扰动有效的$ε$（$m=2$）通过二阶的一般解决方案。我们发现该解满足一个非线性二阶微分方程，作为共动超曲面上线性曲率扰动方程的推广。然后，我们制定了一个一般的方法来匹配的扰动解决方案，精确到$n$ -第阶的扰动内的视界，我们的非线性解决方案，精确到第二阶（$m=2$）的梯度扩展的尺度略大于哈勃半径。在本文中开发的形式主义，使我们能够计算超视界演化的原始非高斯超越所谓的$δN$形式主义或分离宇宙的方法，这是相当于领先的顺序（$m=0$）的梯度展开。特别是，它可以处理的情况下，有一个暂时违反慢滚条件。作为我们的形式主义的应用，我们考虑Starobinsky的模型，这是一个单场模型，由于潜在的斜率急剧变化有一个临时的非慢卷阶段。我们发现，一个大的非高斯性可以产生，即使在超视界尺度，由于这种暂时暂停的慢卷通货膨胀。

英文摘要：

We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a single scalar field with a general kinetic term and a general form of the potential. We employ the ADM formalism and the spatial gradient expansion approach, characterised by $O(ε^m)$, where $ε=1/(HL)$ is a small parameter representing the ratio of the Hubble radius to the characteristic length scale $L$ of perturbations. We obtain the general solution for a full nonlinear version of the curvature perturbation valid up through second-order in $ε$ ($m=2$). We find the solution satisfies a nonlinear second-order differential equation as an extension of the equation for the linear curvature perturbation on the comoving hypersurface. Then we formulate a general method to match a perturbative solution accurate to $n$-th-order in perturbation inside the horizon to our nonlinear solution accurate to second-order ($m=2$) in the gradient expansion on scales slightly greater than the Hubble radius. The formalism developed in this paper allows us to calculate the superhorizon evolution of a primordial non-Gaussianity beyond the so-called $δN$ formalism or separate universe approach which is equivalent to leading order ($m=0$) in the gradient expansion. In particular, it can deal with the case when there is a temporary violation of slow-roll conditions. As an application of our formalism, we consider Starobinsky's model, which is a single field model having a temporary non-slow-roll stage due to a sharp change in the potential slope. We find that a large non-Gaussianity can be generated even on superhorizon scales due to this temporary suspension of slow-roll inflation.

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