空间曲率残局：达到曲率确定的极限
Spatial curvature endgame: Reaching the limit of curvature determination
摘要：
目前对空间曲率的限制表明，它是动态可忽略的：$|Ω_{\rm K}| \lesssim 5 \times 10^{-3}$（95% CL）。然而，忽略它作为宇宙学参数还为时过早，因为在$10^{-4}$水平附近对$Ω_{\rm K}$更严格的约束将为永恒暴胀模型提供有价值的测试，并探索新的大尺度结构现象。这种精度也代表了“曲率地板”，超过这个限度，由于视界尺度扰动的宇宙方差，约束不能得到有意义的改善。在本文中，我们讨论了未来的实验将需要做什么，以测量空间曲率的最大精度。我们保守的预测表明，曲率地板是无法达到的-由一个数量级-即使与第四阶段的实验，除非强假设暗能量演化和$Λ$ CDM参数值。我们还讨论了一些新的问题时，试图约束这样的高精度的全球宇宙学参数$Ω_{\rm K}$。测量到这个水平的曲率将是高精度宇宙学分析中系统学特征的重要验证。
英文摘要：
Current constraints on spatial curvature show that it is dynamically negligible: $|Ω_{\rm K}| \lesssim 5 \times 10^{-3}$ (95% CL). Neglecting it as a cosmological parameter would be premature however, as more stringent constraints on $Ω_{\rm K}$ at around the $10^{-4}$ level would offer valuable tests of eternal inflation models and probe novel large-scale structure phenomena. This precision also represents the "curvature floor", beyond which constraints cannot be meaningfully improved due to the cosmic variance of horizon-scale perturbations. In this paper, we discuss what future experiments will need to do in order to measure spatial curvature to this maximum accuracy. Our conservative forecasts show that the curvature floor is unreachable - by an order of magnitude - even with Stage IV experiments, unless strong assumptions are made about dark energy evolution and the $Λ$CDM parameter values. We also discuss some of the novel problems that arise when attempting to constrain a global cosmological parameter like $Ω_{\rm K}$ with such high precision. Measuring curvature down to this level would be an important validation of systematics characterisation in high-precision cosmological analyses.
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