arXiv 2012.036162020-12-07astro-ph.COcs.LGhep-thmath.AT

大尺度宇宙中原初物理学的拓扑学回声

Topological Echoes of Primordial Physics in the Universe at Large Scales

Gravitation Astroparticle Physics Amsterdam (GRAPPA)（阿姆斯特丹引力天体粒子物理研究所（GRAPPA））；Institute for Theoretical Physics Amsterdam（阿姆斯特丹理论物理研究所）；University of Amsterdam（阿姆斯特丹大学）；IFPU Trieste（的里雅斯特IFPU）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）

Alex Cole, Matteo Biagetti, Gary Shiu

备注：: Condensed version of arXiv:2009.04819, presented at NeurIPS 2020 Workshop "Topological Data Analysis and Beyond." Companion code available at https://gitlab.com/mbiagetti/persistent_homology_lss

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摘要：

我们提出了一个管道，通过持久的同源性在宇宙学中的初始条件的特征和约束。我们感兴趣的宇宙学观测是大尺度结构的宇宙网，初始条件是原始密度扰动的非高斯性。我们计算持久性图和派生的统计模拟的暗物质晕高斯和非高斯初始条件。出于计算原因并与实验观察相联系，我们的管道在完整模拟的子框中计算持久性，并且模拟被二次采样为均匀的晕圈数。我们使用具有大NG（$f_{\rm NL}^{\rm loc}=250$）的模拟作为用于识别具有轻度NG（$f_{\rm NL}^{\rm loc}=10$）的数据的模板，并且在大小为$40~(\textrm{Gpc/h})^{3}$的几个立方体积上运行流水线，我们在体积的$\sim 85\%$上的$97.5\%$置信度下检测$f_{\rm NL}^{\rm loc}=10$，以获得我们的最佳单个统计量。在整个过程中，我们受益于拓扑特征作为统计推断输入的可解释性，这使我们能够与以前的第一性原理计算联系起来，并做出新的预测。

英文摘要：

We present a pipeline for characterizing and constraining initial conditions in cosmology via persistent homology. The cosmological observable of interest is the cosmic web of large scale structure, and the initial conditions in question are non-Gaussianities (NG) of primordial density perturbations. We compute persistence diagrams and derived statistics for simulations of dark matter halos with Gaussian and non-Gaussian initial conditions. For computational reasons and to make contact with experimental observations, our pipeline computes persistence in sub-boxes of full simulations and simulations are subsampled to uniform halo number. We use simulations with large NG ($f_{\rm NL}^{\rm loc}=250$) as templates for identifying data with mild NG ($f_{\rm NL}^{\rm loc}=10$), and running the pipeline on several cubic volumes of size $40~(\textrm{Gpc/h})^{3}$, we detect $f_{\rm NL}^{\rm loc}=10$ at $97.5\%$ confidence on $\sim 85\%$ of the volumes for our best single statistic. Throughout we benefit from the interpretability of topological features as input for statistical inference, which allows us to make contact with previous first-principles calculations and make new predictions.

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