The baryon acoustic oscillations (BAO) provide an important bridge between the early universe and the expansion history at late times. While the BAO has primarily been used as a standard ruler, it also encodes recombination era physics, as demonstrated by a recent measurement of the neutrino-induced phase shift in the BAO feature. In principle, these measurements offer a novel window into physics at the time of baryon decoupling. However, our analytic understanding of the BAO feature is limited, particularly for the range of Fourier modes measured in surveys. As a result, it is unclear what the BAO phase teaches us about the early universe beyond what is already known from the cosmic microwave background (CMB). In this paper, we provide a more complete (semi-)analytic treatment of the BAO on observationally relevant scales. In particular, we compute corrections to the frequency and phase of the BAO feature that arise from higher order effects which occur in the tight coupling regime and during baryon decoupling. The total phase shift we find is comparable to a few percent shift in the BAO scale (frequency) and thus relevant in current data. Our results include an improved analytic calculation of the neutrino induced phase shift template that is in close agreement with the numerically determined template used in measurements of the CMB and BAO.

中文翻译：

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可观察尺度上的 BAO 阶段

重子声波振荡（BAO）在早期宇宙和晚期膨胀历史之间架起了重要的桥梁。虽然 BAO 主要用作标准尺子，但它也编码了重组时代的物理学，正如最近对 BAO 特征中中微子引起的相移的测量所证明的那样。原则上，这些测量为重子解耦时的物理学提供了一个新的窗口。然而，我们对 BAO 特征的分析理解是有限的，特别是对于调查中测量的傅立叶模式范围。因此，除了从宇宙微波背景 (CMB) 已知的知识之外，还不清楚 BAO 阶段教给我们什么关于早期宇宙的知识。在本文中，我们在观察相关的尺度上对 BAO 进行了更完整的（半）分析处理。特别是，我们计算了对 BAO 特征的频率和相位的修正，这些修正是由在紧耦合机制和重子解耦期间发生的高阶效应引起的。我们发现的总相移与 BAO 标度（频率）的几个百分比相移相当，因此与当前数据相关。我们的结果包括对中微子诱导相移模板的改进分析计算，该模板与用于测量 CMB 和 BAO 的数值确定模板非常一致。