距离和生长探测器在检验时间变化暗能量中的互补作用
Complementary Roles of Distance and Growth Probes in Testing Time-Varying Dark Energy
AI总结：
本研究通过分析距离和生长探测器的信息特性，揭示了它们在检验时间变化暗能量中的互补作用，发现生长探测器在高精度下能补充距离探测器的信息。
摘要：
距离测量长期以来一直是宇宙膨胀历史和暗能量性质的主要观测约束。然而，由于这些可观测变量依赖于Hubble率的累积径向积分，它们对暗能量方程状态时间依赖特征的敏感性本质上是有限的。在本工作中，我们从信息的角度出发，利用由距离、膨胀率和生长可观测变量构建的Fisher信息矩阵的特征结构，探讨了这一限制。我们表明，距离和膨胀率数据通常会产生一个强烈分层的Fisher谱，主要由单一信息模式主导，反映了对暗能量时间变化的不可逆敏感性丧失。这种行为可以直接追溯到几何可观测变量的积分内核结构。相比之下，生长测量通过微分动力学响应，并可以引入额外的独立信息方向。利用受控的模拟数据和代表下一代实验的调查型配置，我们发现生长信息的影响不仅取决于其名义精度，还取决于数据协方差的结构。在简化模拟设置中，生长测量可以在中等精度下部分激活第二个信息方向。然而，在类似Euclid的配置中，信息仍然基本上是一维的，直到生长精度达到百分比水平，此时第二个模式迅速出现。这些结果阐明了距离和生长探测器的互补作用，并提供了一个模型无关的标准，用于评估宇宙学约束在动态暗能量中的物理内容。
英文摘要：
Distance measurements have long provided the primary observational constraints on the expansion history of the Universe and the properties of dark energy. However, because such observables depend on cumulative line-of-sight integrals over the Hubble rate, their sensitivity to time-dependent features of the dark energy equation of state is intrinsically limited. In this work, we examine this limitation from an information-based perspective using the eigenvalue structure of the Fisher information matrix constructed from distance, expansion rate, and growth observables. We show that distance and expansion-rate data generically produce a strongly hierarchical Fisher spectrum dominated by a single information mode, reflecting an irreducible loss of sensitivity to temporal variations in dark energy. This behavior can be traced directly to the integrated kernel structure of geometric observables. Growth measurements, by contrast, respond through differential dynamics and can introduce additional independent information directions. Using both controlled mock data and survey-like configurations representative of next-generation experiments, we find that the impact of growth information depends not only on its nominal precision but also on the structure of the data covariance. In simplified mock setups, growth measurements can partially activate a second information direction even at moderate precision. In Euclid-like configurations, however, the information remains effectively one-dimensional until growth precision reaches the percent level, below which a second mode emerges rapidly. These results clarify the complementary roles of distance and growth probes and provide a model-independent criterion for assessing the physical content of cosmological constraints on dynamical dark energy.
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