宇宙学观测量的二阶规范不变形式：规范不变性的完全验证
Second-order gauge-invariant formalism for the cosmological observables: Complete verification of their gauge-invariance
摘要：
考虑到所有的相对论效应，我们发展了描述宇宙学观测量的完全非线性规范不变形式，并给出了与光传播和观测相关的二阶微扰表达式，而不选择规范条件。这是第一次，我们已经进行了一个完整的验证，我们的二阶表达式的有效性，通过比较他们的规范变换性能从两个独立的方法：一个直接从他们的表达式中获得的度量扰动和其他预期从他们的非线性关系。宇宙学观测量的表达式，如星系团和光度距离是不变的，在观测位置的规范不变。我们比较我们的结果与以前的工作，并讨论微扰表达式的差异。我们的二阶规范不变形式主义构成了精密宇宙学时代的重要一步，它在未来的应用将在超越功率谱和探索早期宇宙方面发挥至关重要的作用。
英文摘要：
Accounting for all the relativistic effects, we have developed the fully nonlinear gauge-invariant formalism for describing the cosmological observables and presented the second-order perturbative expressions associated with light propagation and observations without choosing a gauge condition. For the first time, we have performed a complete verification of the validity of our second-order expressions by comparing their gauge-transformation properties from two independent methods: one directly obtained from their expressions in terms of metric perturbations and the other expected from their nonlinear relations. The expressions for the cosmological observables such as galaxy clustering and the luminosity distance are invariant under diffeomorphism and gauge-invariant at the observed position. We compare our results to the previous work and discuss the differences in the perturbative expressions. Our second-order gauge-invariant formalism constitutes a major step forward in the era of precision cosmology and its applications in the future will play a crucial role for going beyond the power spectrum and probing the early universe.
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