arXiv 1402.19672014-02gr-qcastro-ph.COmath-phmath.CAmath.DSmath.MP

双流体Bianchi I型宇宙的动力学

The Dynamics of a Two-Fluid Bianchi Type I Universe

Ikjyot Singh Kohli, Michael C. Haslam

摘要：

本文采用基于正交标架方法的动力系统方法研究了双流体非倾斜Bianchi I型宇宙学模型的动力学行为。在我们的模型中，其中一种流体是具有体粘滞性的流体，而另一种流体则扮演宇宙学常数的角色，并代表非负的真空能量。首先，我们完成了详细的固定点分析的系统，提供有关本地汇，源和鞍。然后，我们使用拓扑方法通过寻找$α$ -和$ω$ -极限集来分析动力系统的全局特征。所发现的不动点是一个平坦的FLRW宇宙，一个爱因斯坦-德西特宇宙，一个德西特宇宙，一个真空和非真空能量的混合FLRW宇宙，和一个卡斯纳宇宙。然后，我们找到每个平衡点是一个鞍，汇，或源的条件，并试图描述的全球和过去的渐近行为的模型相对于每个固定点。我们发现的具有真空和非真空能量的平坦FLRW宇宙解对于模拟当今宇宙显然是至关重要的。特别地，我们证明了这个平衡点是动力系统的一个局部汇和一个鞍点，所以在未来有轨道接近这个平衡点。因此，存在一个时间段，在这个时间段内，我们的宇宙学模型将各向同性化，并且除了真空和非真空能量的存在之外，还与当今观测到的宇宙微波背景的高度各向同性相兼容。

英文摘要：

We use a dynamical systems approach based on the method of orthonormal frames to study the dynamics of a two-fluid, non-tilted Bianchi Type I cosmological model. In our model, one of the fluids is a fluid with bulk viscosity, while the other fluid assumes the role of a cosmological constant and represents nonnegative vacuum energy. We begin by completing a detailed fixed-points analysis of the system which gives information about the local sinks, sources and saddles. We then proceeded to analyze the global features of the dynamical system by using topological methods by finding the $α$- and $ω$-limit sets. The fixed points found are a flat FLRW universe, an Einstein-de Sitter universe, a de Sitter universe, a mixed FLRW universe with both vacuum and non-vacuum energy, and a Kasner universe. We then find conditions for which each equilibrium point was a saddle, sink, or source, and attempt to describe the global and past asymptotic behaviour of the model with respect to each fixed point. The flat FLRW universe solution we found with both vacuum and non-vacuum energy is clearly of primary importance with respect to modelling the present-day universe. In particular, we show that this equilibrium point is a local sink and a saddle of the dynamical system, so there are orbits that approach this equilibrium point in the future. Therefore, there exists a time period for which our cosmological model will isotropize and be compatible with present-day observations of a high degree of isotropy of the cosmic microwave background in addition to the existence of both vacuum and non-vacuum energy.

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