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arXiv 1206.0618astro-ph.COgr-qc
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Einstein-de Sitter和ΛCDM宇宙学球形坍缩模型中的相对论维里化

Relativistic virialization in the Spherical Collapse model for Einstein-de Sitter and ΛCDM cosmologies

Sven Meyer, Francesco Pace, Matthias Bartelmann

摘要:

球形坍缩是研究不同DE模型和重力理论下构造形成的一个成功的半解析模型。然而,维里化的过程通常是在经典力学的维里定理的基础上研究的。本文基于均匀、理想流体球的TOV解,为Einstein-de Sitter和ΛCDM宇宙学构造了一个完全广义相对论维里定理.我们调查的准确性,经典的维里化宇宙学尺度的研究,并考虑维里化从一个更基本的角度来看。自始至终,我们都停留在广义相对论和FLRW模型的范畴内。建立了维里化方程,并对维里半径y_{vir}进行了数值求解,由此直接得到了维里超密度Δ {V}。在后牛顿框架中的领导阶校正推导和量化。此外,在应用中的问题,这种形式主义的动态DE模型指出,并明确讨论。结果表明,在弱场极限下,后牛顿展开的首阶项的相对贡献为10 - 3%,精确地再现了Wang & Steinhardt(1998)的解.除了小的修正,该方法可以从更基本的角度洞察男性化的过程。

英文摘要:

Spherical collapse has turned out to be a successful semi-analytic model to study structure formation in different DE models and theories of gravity. Nevertheless, the process of virialization is commonly studied on the basis of the virial theorem of classical mechanics. In the present paper, a fully generally-relativistic virial theorem based on the Tolman-Oppenheimer-Volkoff (TOV) solution for homogeneous, perfect-fluid spheres is constructed for the Einstein-de Sitter and ΛCDM cosmologies. We investigate the accuracy of classical virialization studies on cosmological scales and consider virialization from a more fundamental point of view. Throughout, we remain within general relativity and the class of FLRW models. The virialization equation is set up and solved numerically for the virial radius, y_{vir}, from which the virial overdensity Δ_{V} is directly obtained. Leading order corrections in the post-Newtonian framework are derived and quantified. In addition, problems in the application of this formalism to dynamical DE models are pointed out and discussed explicitly. We show that, in the weak field limit, the relative contribution of the leading order terms of the post-Newtonian expansion are of the order of 10^{-3}% and the solution of Wang & Steinhardt (1998) is precisely reproduced. Apart from the small corrections, the method could provide insight into the process of virialization from a more fundamental point of view.

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