Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation
Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation
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比较结构形成的广义相对论和牛顿计算
DOI：
10.1103/physrevd.97.043509
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发表时间：
2017
影响因子：
5
通讯作者：
Tom Abel
中科院分区：
文献类型：
--
作者：
W. East;R. Wojtak;Tom Abel
在研究宇宙结构形成的标准方法中，假设宇宙的整体膨胀是均匀的，而不均匀的引力效应完全编码在牛顿势能中。一个正在讨论的话题是，这在多大程度上完全捕捉到了广义相对论所规定的动力学，特别是在精密宇宙学的时代。为了定量地评估这一点，我们直接将标准的N体牛顿计算与爱因斯坦方程的全数值解进行比较，对于具有不同量级初始不均匀的冷物质，其尺度可与哈勃视界相媲美。我们分析了密度、光度距离和相对于基准观测者定义的其他量的演化的差异。这是通过重建由牛顿量决定的有效时空和物质场，并注意区分数值分辨率的影响来实现的。我们发现，完全广义相对论计算和牛顿计算显示出很好的一致性，甚至很好地进入了非线性区域。它们只有在弱重力假设失效的地区才有显著差异，当考虑扰动超过标准值的极端情况时，就会出现这种情况。
In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic of ongoing debate is to what degree this fully captures the dynamics dictated by general relativity, especially in the era of precision cosmology. To quantitatively assess this, we directly compare standard N-body Newtonian calculations to full numerical solutions of the Einstein equations, for cold matter with various magnitude initial inhomogeneities on scales comparable to the Hubble horizon. We analyze the differences in the evolution of density, luminosity distance, and other quantities defined with respect to fiducial observers. This is carried out by reconstructing the effective spacetime and matter fields dictated by the Newtonian quantities, and by taking care to distinguish effects of numerical resolution. We find that the fully general relativistic and Newtonian calculations show excellent agreement, even well into the nonlinear regime. They only notably differ in regions where the weak gravity assumption breaks down, which arise when considering extreme cases with perturbations exceeding standard values.