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arXiv 1004.0773gr-qcastro-ph.CO
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非齐次Lambda-CDM模型的动力系统研究

A dynamical systems study of the inhomogeneous Lambda-CDM model

Roberto A. Sussman, German Izquierdo

摘要:

我们考虑具有正的宇宙学常数$Λ$的球对称非均匀尘埃模型,由Lemaitre-Tolman-Bondi度规给出。这些配置提供了一个简单的,但有用的推广的Lambda-CDM模型描述冷暗物质(CDM)和一个Lambda项,这似乎适合目前的宇宙学观测。这些模型的动力学可以完全描述标量演化方程,可以给出一个适当的动力学系统的形式与4维相空间,其临界点和不变子空间进行检查和分类。各种配置的相空间演化的详细研究,通过两个2维子空间:一个投影到不变的齐次子空间与Lambda CDM解决方案与FLRW度量,和一个投影到一个子空间所产生的适当定义的波动,传达不均匀性的影响。我们研究的情况下,与永久的膨胀,弹跳和游荡的行为,以及配置与“混合”的运动模式,如在一个不断扩大的背景塌陷区。在所有情况下,相空间轨迹出现和收敛到稳定的过去和未来的吸引子在定性类似的方式,在FLRW限制的情况下。然而,我们可以确定在这两个投影的相空间中的各种定性功能缺席的FLRW限制,可以是有用的玩具模型的天体物理和宇宙学的不均匀性的建设。

英文摘要:

We consider spherically symmetric inhomogeneous dust models with a positive cosmological constant, $Λ$, given by the Lemaitre-Tolman-Bondi metric. These configurations provide a simple but useful generalization of the Lambda-CDM model describing cold dark matter (CDM) and a Lambda term, which seems to fit current cosmological observations. The dynamics of these models can be fully described by scalar evolution equations that can be given in the form of a proper dynamical system associated with a 4-dimensional phase space whose critical points and invariant subspaces are examined and classified. The phase space evolution of various configurations is studied in detail by means of two 2-dimensional subspaces: a projection into the invariant homogeneous subspace associated with Lambda-CDM solutions with FLRW metric, and a projection into a subspace generated by suitably defined fluctuations that convey the effects of inhomogeneity. We look at cases with perpetual expansion, bouncing and loitering behavior, as well as configurations with "mixed" kinematic patters, such as a collapsing region in an expanding background. In all cases, phase space trajectories emerge from and converge to stable past and future attractors in a qualitatively analogous way as in the case of the FLRW limit. However, we can identify in both projections of the phase space various qualitative features absent in the FLRW limit that can be useful in the construction of toy models of astrophysical and cosmological inhomogeneities.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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