Relativistic Euler equations in cosmologies with nonlinear structures
Relativistic Euler equations in cosmologies with nonlinear structures
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DOI：
10.1103/physrevd.98.103516
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发表时间：
2018-07
影响因子：
5
通讯作者：
Christopher S. Gallagher;T. Clifton
中科院分区：
文献类型：
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作者：
Christopher S. Gallagher;T. Clifton
我们考虑一种新的宇宙学微扰理论的变体，它是专门设计来包括100 Mpc尺度上的非线性密度对比，同时仍然允许更大尺度上的线性波动。这个理论被用来推导现实宇宙学场景中的欧拉流体动力学的相对论方程，其中包含辐射和宇宙学常数，以及被允许聚集成星系和星系团的物质。这些方程可以用来在小尺度非线性结构的存在下，以及在一直到视界和更远的尺度上，演化能量密度和速度。这些方程的首阶部分再现了预期的牛顿方程，而随后的阶则规定了相对论修正。我们证明，这些演化方程是一致的，保持爱因斯坦的约束，因此，系统作为一个整体是数学适定性。我们得到的相对论修正被发现表现出不同尺度上的扰动之间的非平凡的相互作用，以及标量，矢量和张量模式的混合。它们偏离了后弗里德曼和标准宇宙学微扰理论方法中出现的结果，并指向了新的相对论效应，这些效应可以通过即将到来的超大规模巡天测量。
We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used to derive the relativistic equations of Eulerian hydrodynamics in realistic cosmological scenarios that contain radiation and a cosmological constant, as well as matter that has been allowed to clump into galaxies and clusters of galaxies. These equations can be used to evolve energy densities and velocities in the presences of small-scale non-linear structures, and on scales all the way up to the horizon and beyond. The leading-order part of these equations reproduces the expected Newtonian equations, while subsequent orders prescribe relativistic corrections. We demonstrate that these evolution equations are consistent with maintaining the Einstein constraints, and hence that the system as a whole is mathematically well posed. The relativistic corrections that we derive are found to exhibit non-trivial interactions between perturbations on different scales, as well as the mixing of scalar, vector and tensor modes. They deviate from those that occur in both post-Friedmann and standard cosmological perturbation theory approaches, and point towards new relativistic effects that could be measurable by upcoming ultra-large-scale surveys.