论文标题
大规模结构的持久性I：原始非高斯性
The Persistence of Large Scale Structures I: Primordial non-Gaussianity
论文作者
论文摘要
我们开发了一个分析管道，以表征大规模结构的拓扑并根据持续的同源性提取宇宙学约束。持续的同源性是一种拓扑数据分析的技术，可以量化数据集的多尺寸拓扑，在我们的情况下，统一了集群，细丝循环和宇宙空隙对宇宙学约束的贡献。我们使用一组N体模拟作为真实数据分析的代理，描述了该方法如何捕获原始局部非高斯语对暗物质光环的延迟分布的烙印。对于我们最好的单个统计数据，运行管道上的几立方图$ 40〜（\ rm {gpc/h}）^{3} $，我们检测到$ f _ {\ rm nl}^{\ rm nl}^{\ rm loc} = 10 $ at $ 97.5 \％$ 97.5 \％$ \％$ \ sim 85 \ sim 85 $ \％$ \％$ \％。此外，我们测试了解决$ f _ {\ rm nl}^{\ rm loc} $的拓扑特征与$σ_8$的变化之间的拓扑特征之间的能力，并认为正确地识别非零$ f _ {\ rm nl}^{\ rm loc} $在这种情况下可以通过一个方法来识别非零$ f _ {\ rm nl}^loc} $。我们的方法依赖于$ \ Mathcal {O}（10）$ MPC/h的信息，这是一种相对于常用方法（例如Halo/Galaxy Power Spectrum中的比例依赖性偏差）的补充规模。因此，尽管仍然需要大量的数量，但我们的方法不需要采样长波长模式来限制原始非高斯性。此外，我们的统计数据是可解释的：我们能够在某些范围内重现先前的结果，并为未开发的可观察物进行了新的预测，例如模拟框中的暗物质晕圈形成的细丝循环。
We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies the multiscale topology of a data set, in our context unifying the contributions of clusters, filament loops, and cosmic voids to cosmological constraints. We describe how this method captures the imprint of primordial local non-Gaussianity on the late-time distribution of dark matter halos, using a set of N-body simulations as a proxy for real data analysis. For our best single statistic, running the pipeline on several cubic volumes of size $40~(\rm{Gpc/h})^{3}$, we detect $f_{\rm NL}^{\rm loc}=10$ at $97.5\%$ confidence on $\sim 85\%$ of the volumes. Additionally we test our ability to resolve degeneracies between the topological signature of $f_{\rm NL}^{\rm loc}$ and variation of $σ_8$ and argue that correctly identifying nonzero $f_{\rm NL}^{\rm loc}$ in this case is possible via an optimal template method. Our method relies on information living at $\mathcal{O}(10)$ Mpc/h, a complementary scale with respect to commonly used methods such as the scale-dependent bias in the halo/galaxy power spectrum. Therefore, while still requiring a large volume, our method does not require sampling long-wavelength modes to constrain primordial non-Gaussianity. Moreover, our statistics are interpretable: we are able to reproduce previous results in certain limits and we make new predictions for unexplored observables, such as filament loops formed by dark matter halos in a simulation box.
