Averaging in spherically symmetric cosmology
Averaging in spherically symmetric cosmology
复制标题
DOI：
10.1103/physrevd.75.043506
复制
发表时间：
2007-02-01
影响因子：
5
通讯作者：
Pelavas, N.
中科院分区：
文献类型：
--
作者：
Coley, A. A.;Pelavas, N.
宇宙学中的平均问题具有根本的重要性。当应用于研究宇宙学演化时，宏观引力理论（MG）可以被视为广义相对论的远距离修正。在宇宙学平均化问题的MG方法中，用适当的引力关联项修正了宇宙尺度下的爱因斯坦场方程。本文研究了球对称宇宙学模型中的平均问题。也就是说，我们将采用微观方程，并进行平均过程，以确定这种情况下关联张量的精确形式。特别地，在保体积坐标系下，我们在对非均匀引力场和物质分布形式的合理假设下，计算了相关张量的形式。我们发现，在Friedmann-Lemaitre-Robertson-Walker（FLRW）背景中的相关张量必须是空间曲率的形式。不均匀性和空间平均，通过这个空间曲率修正项，可以有一个非常显着的动力学效应的宇宙和宇宙学观测的动力学;特别是，我们讨论是否空间平均可能导致一个更保守的解释所观察到的宇宙加速（没有引进外来的暗物质场）。我们还发现，非FLRW背景的相关张量可以解释为空间曲率和各向异性流体的总和。这可能会导致有趣的天体物理尺度上的平均效应。我们还讨论了平均的非均匀Lemaitre-Tolman-Bondi解决方案，以及在FLRW背景下的线性扰动（即，反反应）的计算结果，这支持了分析的主要结论。
The averaging problem in cosmology is of fundamental importance. When applied to study cosmological evolution, the theory of macroscopic gravity (MG) can be regarded as a long-distance modification of general relativity. In the MG approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We study the averaging problem within the class of spherically symmetric cosmological models. That is, we shall take the microscopic equations and effect the averaging procedure to determine the precise form of the correlation tensor in this case. In particular, by working in volume-preserving coordinates, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. We find that the correlation tensor in a Friedmann-Lemaitre-Robertson-Walker (FLRW) background must be of the form of a spatial curvature. Inhomogeneities and spatial averaging, through this spatial curvature correction term, can have a very significant dynamical effect on the dynamics of the Universe and cosmological observations; in particular, we discuss whether spatial averaging might lead to a more conservative explanation of the observed acceleration of the Universe (without the introduction of exotic dark matter fields). We also find that the correlation tensor for a non-FLRW background can be interpreted as the sum of a spatial curvature and an anisotropic fluid. This may lead to interesting effects of averaging on astrophysical scales. We also discuss the results of averaging an inhomogeneous Lemaitre-Tolman-Bondi solution as well as calculations of linear perturbations (that is, the backreaction) in an FLRW background, which support the main conclusions of the analysis.