结构形成的Einstein-Vlasov计算
Einstein-Vlasov Calculations of Structure Formation
摘要：
我们研究了膨胀宇宙中的小不均匀性的动力学坍缩，形成束缚结构使用完整的解决方案的Einstein-Vlasov（N体）方程。我们比较这些标准的牛顿N-体的解决方案，使用相对于基准观察员，以约束相对论效应定义的数量。我们专注于简化的初始条件，包含一个有限的范围内的长度尺度，但不同的不均匀性从小幅度，牛顿和广义相对论计算同意得很好，大幅度，其中背景度量接收一阶修正。对于大的不均匀性，我们发现，超密度的崩溃往往发生在牛顿计算相对于完全广义相对论的。即使在这种极端的状态下，在大引力势和速度区域之外的时空演化差异也很小。对于标准的宇宙学值，我们证实了牛顿N体模拟的鲁棒性，以模拟大尺度扰动和相关的宇宙方差的局部膨胀率。
英文摘要：
We study the dynamics of small inhomogeneities in an expanding universe collapsing to form bound structures using full solutions of the Einstein-Vlasov (N-body) equations. We compare these to standard Newtonian N-body solutions using quantities defined with respect to fiducial observers in order to bound relativistic effects. We focus on simplified initial conditions containing a limited range of length scales, but vary the inhomogeneities from small magnitude, where the Newtonian and general-relativistic calculations agree quite well, to large magnitude, where the background metric receives an order one correction. For large inhomogeneities, we find that the collapse of overdensities tends to happen faster in Newtonian calculations relative to fully general-relativistic ones. Even in this extreme regime, the differences in the spacetime evolution outside the regions of large gravitational potential and velocity are small. For standard cosmological values, we corroborate the robustness of Newtonian N-body simulations to model large scale perturbations and the related cosmic variance in the local expansion rate.
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