利用数值相对论模拟从初始曲率扰动研究结构形成与准球对称坍缩
Structure formation and quasi-spherical collapse from initial curvature perturbations with numerical relativity simulations
AI总结：
本文利用数值相对论模拟ΛCDM宇宙中基于初始曲率扰动的非线性结构形成，验证Top-Hat球对称坍缩模型对过密区域演化的适用性，并引入Petrov类型动态分类方法刻画时空几何与引力波产生。
摘要：
我们利用数值相对论模拟来描述ΛCDM宇宙学中非线性结构形成期间的时空演化。完全非线性的初始条件设置在初始红移z≈300处，直接基于通常用于模拟早期宇宙涨落的规范不变共动曲率扰动$\mathcal{R}_c$。给$\mathcal{R}_c$赋予一个简单的三维正弦结构后，我们得到一个准球对称过密区域的晶格，代表通过纤维状结构连接并被空洞包围的理想化暗物质晕。该结构在同步共动规范中实现，使用CDM的无压理想流体（尘埃）描述，然后利用Einstein Toolkit代码对其进行完全演化。借此，我们考察Top-Hat球对称均匀坍缩模型是否能很好地描述过密区域的坍缩。我们发现Top-Hat模型是峰值演化的极好近似，我们观测到剪切可以忽略，并且当线性密度对比度达到预测的临界值$δ^{(1)}_C =1.69$时坍缩发生。此外，我们刻画了回转边界的向外膨胀，并展示了它如何依赖于物质的初始分布，发现它在更密集的方向上更快，将越来越多的物质纳入内落区域。利用EBWeyl代码[1]，我们考察了Weyl张量电部分和磁部分的分布，发现它们分别沿纤维状结构及其周围更强。我们引入了一种按Petrov类型动态分类不同区域的方法。借此，我们发现时空处处为Petrov I型，正如预期，但我们能够识别主导阶类型，发现随着非线性增长，不同类型之间发生转变，并伴随引力波的产生。
英文摘要：
We use numerical relativity simulations to describe the spacetime evolution during nonlinear structure formation in $Λ$CDM cosmology. Fully nonlinear initial conditions are set at an initial redshift $z\approx 300$, based directly on the gauge invariant comoving curvature perturbation $\mathcal{R}_c$ commonly used to model early-universe fluctuations. Assigning a simple 3-D sinusoidal structure to $\mathcal{R}_c$, we then have a lattice of quasi-spherical over-densities representing idealised dark matter halos connected through filaments and surrounded by voids. This structure is implemented in the synchronous-comoving gauge, using a pressureless perfect fluid (dust) description of CDM, and then it is fully evolved with the Einstein Toolkit code. With this, we look into whether the Top-Hat spherical and homogeneous collapse model provides a good description of the collapse of over-densities. We find that the Top-Hat is an excellent approximation for the evolution of peaks, where we observe that the shear is negligible and collapse takes place when the linear density contrast reaches the predicted critical value $δ^{(1)}_C =1.69$. Additionally, we characterise the outward expansion of the turn-around boundary and show how it depends on the initial distribution of matter, finding that it is faster in denser directions, incorporating more and more matter in the infalling region. Using the EBWeyl code [1] we look at the distribution of the electric and magnetic parts of the Weyl tensor, finding that they are stronger along and around the filaments, respectively. We introduce a method to dynamically classify different regions in Petrov types. With this, we find that the spacetime is of Petrov type I everywhere, as expected, but we can identify the leading order type, finding a transition between different types as non-linearity grows, with production of gravitational waves.
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