标题： 多尺度结构的宇宙平均化：关于叶状结构、规范和反冲效应 显示英文标题

标题： Cosmic averaging over multiscaled structure: on foliations, gauges and backreaction

摘要： 自兆帕斯卡尺度的宇宙结构变得非线性以来，加速宇宙膨胀占据主导地位这一观测结果似乎是一个非凡的巧合，除非这种加速是由结构的出现所驱动。这催生了关于引力回反应这一有争议概念的提出，通过它不均匀性成为加速膨胀的驱动力。 在研究强非均匀宇宙模型时，标准方法是采用摄动方法或空间平均方法。 在这里我们论证了由于回反应实际上是一种非线性的多尺度现象，摄动方法可能具有有限的有效性。 另一种选择是提议的平均方法。 在这篇论文中，我们证明了隐含的回反应项是人为的，即规范相关的，这可能导致对其重要性产生模棱两可的估计。 在当前的研究中，我们在相对论宇宙学的背景下提出了时空叶层的正式完全几何框架。 在这里，我们展示了固定时空的叶层确定了一种规范的选择。 探讨度规张量与叶层之间的对应关系使我们能够阐明选择叶层的理论含义。 在回反应的背景下，这个形式主义允许我们讨论平均化的问题。 它揭示了空间平均可以诱导出由特定规范选择引起的任意人工回反应项。 迄今为止提出的平均方法都遇到了这个问题。 在我们的叶层框架内，我们可以通过对考虑一组适当的叶层来产生规范不变的平均方法，这些叶层是任何宇宙观测者都能达成一致的。 我们证明了这意味着平均过程的规范不变性。 这使其适用于标准的宇宙学模拟。 显示英文摘要

摘要： The observation that accelerated cosmic expansion is dominant since the Mega-parsec cosmic structure became nonlinear seems like an extraordinary coincidence, unless the acceleration is somehow driven by the emergence of the structure. That has given rise to the controversial concept of a gravitational backreaction through which inhomogeneity becomes a driver of accelerated expansion. The standard route when studying strongly inhomogeneous cosmological models is to take either a perturbative approach or a spatial averaging approach. Here we argue that because backreaction is in fact a nonlinear multiscale phenomenon, perturbative approaches may have a limited validity. The alternative is the proposed averaging approach. In this paper we demonstrate that the implied backreaction terms are artificial, that is gauge dependent, which may easily cause ambiguous estimates of its significance. In the current study, we forward a formal fully geometric framework of cosmic foliations in the context of relativistic cosmology. Here we show that fixing a foliation of spacetime determines a choice of gauge. Addressing the correspondence between the metric tensor and the foliation allows us to clarify the theoretical implications of choosing a foliation. Within the context of backreaction, this formalism allows us to discuss the complications of averaging. It reveals that spatial averaging can induce artificial backreaction terms that arise from any specific choice of gauge. Averaging methods presented so far all encounter this problem. Within our foliation framework, we can produce a gauge invariant method of averaging by considering a group of proper time foliations which any cosmic observe can agree upon. We demonstrate that this implies the gauge invariance of the averaging procedure. This makes it applicable to standard cosmological simulations.