标题： 在膨胀宇宙中不膨胀的东西：一个非常简单的模型 显示英文标题

标题： On what does not expand in an expanding universe: a very simple model

摘要： 随着宇宙的膨胀，星系之间的分离增大，但星系本身和较小的束缚结构并不会增长。 准确描述宇宙结构的动力学需要广义相对论的全部理论工具。 然而，为了对在膨胀宇宙中什么不膨胀有一个相当满意的理解，只需以简谐振子作为束缚系统的原型就足够了。 更精确地说，我们证明，在膨胀宇宙中研究非相对论性简谐振子的量子动力学可以清楚地表明，大多数束缚系统并不参与整体的宇宙膨胀。 该分析是基本的，并表明一个束缚结构是否部分参与膨胀或根本不参与，本质上是由与之相关的特征时间尺度决定的。 显示英文摘要

摘要： As the separation between galaxies increases owing to the expansion of the universe, galaxies themselves and smaller bound structures do not grow. An accurate description of the dynamics of cosmic structures requires the full apparatus of general relativity. In order to gain a fairly satisfactory understanding of what does not expand in an expanding universe, however, it suffices to take the harmonic oscillator as prototype of a bound system. More precisely, we show that a study of the quantum dynamics of a nonrelativistic harmonic oscillator in an expanding universe makes it clear that most bound systems do not take part in the overall cosmic expansion. The analysis is elementary and indicates that whether a bound structure partakes in the expansion partially or not at all is essentially determined by a characteristic time scale associated with it.