标题： 谱表示与宇宙学中的平均化问题 显示英文标题

标题： Spectral Representation and the Averaging Problem in Cosmology

摘要： 我们研究宇宙学中的平均问题，将其视为引入空间之间距离的问题。 我们首先引入谱距离，这是一种基于拉普拉斯算子谱定义的空间接近性度量。 然后我们定义一个空间 S，即所有配备谱距离的空间的集合。 我们认为这个空间 S 可以被视为一个度量空间，并且还具有其他理想的性质。 这些事实使空间 S 成为时空物理的合适场所。 我们将谱框架应用于平均问题： 我们根据谱表示概述了模型拟合过程，并简要讨论了如何用此方案分析平均过程的动力学方面。 在这些分析中，我们自然地引出了装置和尺度依赖的有效宇宙演化概念。 这些观察表明，谱方案似乎适合对宇宙学中的平均问题进行定量分析。 显示英文摘要

摘要： We investigate the averaging problem in cosmology as the problem of introducing a distance between spaces. We first introduce the spectral distance, which is a measure of closeness between spaces defined in terms of the spectra of the Laplacian. Then we define a space S, the space of all spaces equipped with the spectral distance. We argue that this space S can be regarded as a metric space and that it also possess other desirable properties. These facts make the space S a suitable arena for spacetime physics. We apply the spectral framework to the averaging problem: We sketch the model-fitting procedure in terms of the spectral representation, and also discuss briefly how to analyze the dynamical aspects of the averaging procedure with this scheme. In these analyses, we are naturally led to the concept of the apparatus- and the scale-dependent effective evolution of the universe. These observations suggest that the spectral scheme seems to be suitable for the quantitative analysis of the averaging problem in cosmology.