标记功率谱测量什么？微扰理论的启示
What does the Marked Power Spectrum Measure? Insights from Perturbation Theory
摘要：
标记的功率谱能够对宇宙学参数（特别是中微子质量）施加比传统功率谱更严格的约束。除了传统的统计数据之外，它还包含哪些新的信息？通过微扰模型的发展，我们发现，标记诱导的非高斯性，这通常是在小尺度上，和大尺度之间的显着耦合，导致额外的信息内容。该模型是在单回路微扰理论的背景下推导出来的，并通过与各种标记参数的$N$体模拟进行比较来验证。在中等红移，包括大质量中微子宇宙学，理论与模拟吻合得很好。非线性引力效应对大尺度谱的重要性使建模复杂化，因为在低$z$下没有明确定义的理论收敛半径。扩展到更高的微扰阶和有偏见的示踪剂是可能的，通过类似的方法，和一个简单的模型，后者示出产生有前途的结果。对于小的平滑尺度，该理论在红移为零时变得非微扰，高阶项的重要贡献：在实现该工具的全部功能之前，需要对这些进行研究。
英文摘要：
The marked power spectrum is capable of placing far tighter constraints on cosmological parameters (particularly the neutrino mass) than the conventional power spectrum. What new information does it contain beyond conventional statistics? Through the development of a perturbative model, we find that the mark induces a significant coupling between non-Gaussianities, which are usually found on small scales, and large scales, leading to the additional information content. The model is derived in the context of one-loop perturbation theory and validated by comparison to $N$-body simulations across a variety of mark parameters. At moderate redshifts, including for massive neutrino cosmologies, the theory is in good agreement with the simulations. The importance of non-linear gravitational effects on the large-scale spectra complicates the modeling as there is no well-defined convergence radius of the theory at low $z$. Extension to higher perturbative order and biased tracers is possible via a similar approach, and a simple model of the latter is shown to yield promising results. The theory becomes non-perturbative at redshift zero for small smoothing scales, with important contributions from higher-order terms: these will need to be studied before the full power of this tool can be realized.
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