线性区之外的宇宙学关联维数：解析近似与参数敏感性
The Cosmological Correlation Dimension Beyond the Linear Regime: Analytical Approximation and Parameter Sensitivity
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中文总结 AI 辅助
该研究将宇宙学关联维数D2与物质功率谱直接联系，提出基于滤波核有效截断的解析近似，并在w0waCDM模型中进行局部和全局敏感性分析，发现非线性演化降低小尺度D2，截断近似精度优于1%，识别出Omega_m和A_s为关键参数。
中文摘要 AI 辅助
关联维数（$D_2$）提供了对向均匀性过渡的尺度依赖表征，以及对大尺度结构成团性的互补视角。在本工作中，我们研究了其对尺度和红移的完整依赖关系，将$D_2$直接与给定宇宙学模型的物质功率谱联系起来，并基于滤波核的有效截断表示推导出一个近似的解析关系。我们进一步在$w_0w_a$CDM模型内进行了两种互补的局部（基于导数）和全局（基于方差）敏感性分析。总体而言，非线性演化使$D_2$在小尺度上相对于线性预测降低，且该效应在低红移时更为显著。我们的截断近似，采用$k_{\rm cut}=\alpha/r$且$\alpha\simeq 2.39$，在所考虑的代表性情形下，对精确$D_2$的复现精度优于1%。敏感性分析识别出$\Omega_m$和$A_s$分别为线性关联维数及其非线性与线性之比的主导参数，而$w_0$和$w_a$则在非线性贡献中引起尺度和红移依赖的变化。这些结果为表征$D_2$的宇宙学尺度与红移依赖特征及其非线性修正提供了一个框架。
英文摘要
The correlation dimension ($D_2$) provides a scale-dependent characterization of the transition towards homogeneity and a complementary perspective on the clustering of large-scale structure. In this work, we study its full dependence on scales and redshift connecting $D_2$ directly to the matter power spectrum of a given cosmological model, and derive an approximate analytical relation based on an effective cut-off representation of the filtering kernel. We further perform two complementary local (derivative-based) and global (variance-based) sensitivity analyses within the $w_0w_a$CDM model. In general, nonlinear evolution lowers $D_2$ relative to the linear prediction at small scales, with the effect becoming more pronounced at low redshift. Our cut-off approximation, with $k_{\rm cut}=α/r$ and $α\simeq 2.39$, reproduces the exact $D_2$ to better than 1\% for the representative cases considered. The sensitivity analysis identifies $Ω_m$ and $A_s$ as the dominant parameters for the linear correlation dimension and its nonlinear-to-linear ratio, respectively, while $w_0$ and $w_a$ induce scale- and redshift-dependent changes in the nonlinear contribution. These results provide a framework for characterizing the cosmological scale- and redshift-dependent features of $D_2$ and its nonlinear correction.
发表机构
- Universidad Politécnica de Madrid（马德里理工大学）
- Universidad de Salamanca（萨拉曼卡大学）
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