生活在一个非平坦的宇宙：理论形式主义
Living in a Non-Flat Universe: Theoretical Formalism
摘要：
最近对普朗克测量的分析揭示了我们生活在一个非平坦宇宙中的可能性。鉴于人们对非零空间曲率的重新关注，本文重新审视了光在非平坦宇宙中的传播，并为宇宙学探测提供了规范不变的表达式：光度距离、星系团、弱引力透镜和宇宙微波背景各向异性。由于空间度规的位置依赖性，光在非平坦宇宙中的传播要比在平坦宇宙中复杂得多。考虑到所有的相对论效应，包括矢量和张量的贡献，我们推导出宇宙探测器的表达式，并明确验证其规范不变性。我们将我们的结果与以前在非平坦宇宙中的工作进行了比较，如果存在的话，但这项工作代表了对非平坦宇宙中宇宙学探测器的第一次全面调查。我们在非平坦宇宙中的理论形式主义将在即将到来的大规模调查中限制空间曲率方面发挥关键作用。
英文摘要：
Recent analysis of the Planck measurements opened a possibility that we live in a non-flat universe. Given the renewed interest in non-zero spatial curvature, here we re-visit the light propagation in a non-flat universe and provide the gauge-invariant expressions for the cosmological probes: the luminosity distance, galaxy clustering, weak gravitational lensing, and cosmic microwave background anisotropies. With the positional dependence of the spatial metric, the light propagation in a non-flat universe is much more complicated than in a flat universe. Accounting for all the relativistic effects and including the vector and tensor contributions, we derive the expressions for the cosmological probes and explicitly verify their gauge invariance. We compare our results to previous work in a non-flat universe, if present, but this work represents the first comprehensive investigation of the cosmological probes in a non-flat universe. Our theoretical formalism in a non-flat universe will play a crucial role in constraining the spatial curvature in the upcoming large-scale surveys.
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