δN formalism
δN formalism
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δ1N形式主义
DOI：
10.1103/physrevd.87.023530
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发表时间：
2013
影响因子：
5
通讯作者：
杉山尚徳・小松英一郎・二間瀬敏史
中科院分区：
文献类型：
--
作者：
Shimizu;T.;杉山尚徳・小松英一郎・二間瀬敏史
准确理解暴涨期间宇宙扰动的非线性演化对于正确解释宇宙微波背景中非高斯相关性的测量和宇宙的大尺度结构是必要的。 “形式主义”是一种流行且强大的技术，用于计算大规模宇宙学扰动的非线性演化。特别是，它使我们能够计算大尺度的曲率扰动，而无需实际求解扰动场方程。然而，人们常常想知道为什么会出现这种情况。为了使这种方法有效，大尺度上的扰动哈密顿约束和物质场方程必须通过适当的坐标选择，采用与相应的未扰动方程相同的形式。我们发现，当 (1) 无扰动度量由均匀且各向同性的 Friedmann-Lemaître-Robertson-Walker 度量给出时，这是可能的； (2) 在大尺度上并且选择合适的坐标，可以忽略位移向量 () 以及扰动度量的张量扰动的时间依赖性。虽然必须先假设第一个条件，但当 (3) 各向异性应力在大范围内变得可以忽略不计时，就可以满足第二个条件。然而，为了明确地表明第二个条件遵循第三个条件，必须使用引力场方程，因此这一说法可能取决于引力理论的细节。最后，由于形式主义仅使用哈密顿约束和物质场方程，因此它并不优先考虑动量约束。我们表明，动量约束中的误差仅产生 的衰减模式解，并且当满足慢滚条件时误差消失。
Precise understanding of nonlinear evolution of cosmological perturbations during inflation is necessary for the correct interpretation of measurements of non-Gaussian correlations in the cosmic microwave background and the large-scale structure of the Universe. The “formalism” is a popular and powerful technique for computing nonlinear evolution of cosmological perturbations on large scales. In particular, it enables us to compute the curvature perturbationon large scales without actually solving perturbed field equations. However, people often wonder why this is the case. In order for this approach to be valid, the perturbed Hamiltonian constraint and matter-field equations on large scales must, with a suitable choice of coordinates, take on the same forms as the corresponding unperturbed equations. We find that this is possible when (1) the unperturbed metric is given by a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker metric; and (2) on large scales and with a suitable choice of coordinates, one can ignore the shift vector () as well as time dependence of tensor perturbations toof the perturbed metric. While the first condition has to be assumeda priori, the second condition can be met when (3) the anisotropic stress becomes negligible on large scales. However, in order to explicitly show that the second condition follows from the third condition, one has to use gravitational field equations, and thus this statement may depend on the details of the theory of gravitation. Finally, as theformalism uses only the Hamiltonian constraint and matter-field equations, it does nota priorirespect the momentum constraint. We show that the error in the momentum constraint only yields a decaying mode solution for, and the error vanishes when the slow-roll conditions are satisfied.