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arXiv 2011.02440gr-qcastro-ph.COhep-th
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光锥上的宇宙涨落

Cosmological Fluctuations on the Light Cone

Asanka Amarasinghe, Philip D. Mannheim

备注：
21 pages. Final version, to appear in Phys. Rev. D
发表信息：
Phys. Rev. D 103, 103517 (2021)
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摘要：

温伯格在研究宇宙微波背景中的温度波动时注意到，通过观察受扰光子在其上传播的受扰光锥的结构，可以在一定程度上简化计算和洞察。在他的方法温伯格工作在一个特定的规范和专门的波动周围的标准罗伯逊-沃克宇宙学模型与消失的空间三曲率。在本文中，我们推广这种分析提供了一个规范不变的治疗，其中没有选择的规范，并考虑几何与非零空间三曲率。通过使用标量，矢量，张量波动基础，我们发现，相关的规范不变的组合，出现在光锥温度波动没有明确的依赖于空间曲率，即使空间曲率的背景几何是非零的。我们发现，以前没有考虑过，虽然不是太重要，温度波动的观察员必须包括在为了执行规范不变性。除了处理共动时间，我们还处理共形时间，其中任何给定空间三曲率的背景度量可以写成与时间相关的共形因子（共动时间扩展半径写成共形时间）乘以相同空间三曲率的静态罗伯逊-沃克几何。对于光锥上的温度波动，这个保形因子同样地下降。因此，出现在光子温度涨落中的规范不变组合与共形因子或空间三曲率都没有明显的依赖关系。

英文摘要：

In studying temperature fluctuations in the cosmic microwave background Weinberg has noted that some ease of calculation and insight can be achieved by looking at the structure of the perturbed light cone on which the perturbed photons propagate. In his approach Weinberg worked in a specific gauge and specialized to fluctuations around the standard Robertson-Walker cosmological model with vanishing spatial three-curvature. In this paper we generalize this analysis by providing a gauge invariant treatment in which no choice of gauge is made, and by considering geometries with non-vanishing spatial three-curvature. By using the scalar, vector, tensor fluctuation basis we find that the relevant gauge invariant combinations that appear in the light cone temperature fluctuations have no explicit dependence on the spatial curvature even if the spatial curvature of the background geometry is nonvanishing. We find that a not previously considered, albeit not too consequential, temperature fluctuation at the observer has to be included in order to enforce gauge invariance. As well as working with comoving time we also work with conformal time in which a background metric of any given spatial three-curvature can be written as a time-dependent conformal factor (the comoving time expansion radius as written in conformal time) times a static Robertson-Walker geometry of the same spatial three-curvature. For temperature fluctuations on the light cone this conformal factor drops out identically. Thus the gauge invariant combinations that appear in the photon temperature fluctuations have no explicit dependence on either the conformal factor or the spatial three-curvature at all.

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