论文标题
三种流体宇宙学模型的动态系统分析：不变的歧管方法
Dynamical System Analysis of a Three Fluid Cosmological Model : An Invariant Manifold approach
论文作者
论文摘要
本文认为，在弗里德曼·罗伯特森 - 沃克森·莱梅特雷·弗拉特里（Friedmann-Robertson-Walker-Lemaitre Flat Spacetime）的背景下，由非相互作用的暗物质，暗能量和重型物质组成的三流体宇宙学模型。已经假定暗物质采用灰尘的形式，而深色能量是具有指数潜力的精髓（真实）标量场。进一步假设，重型物质是带有状态压缩方程的完美液体。在变量进行了一些合适的更改之后，该模型的字段方程采用自主动力系统的形式。然后，考虑所有可能的参数（Baryonic物质的绝热指数和由暗能量电位产生的参数）值以及双曲线和非纤维性临界点的情况。对于非纤维临界点，应用不变的流形理论（中心歧管方法）。最后，产生了各种拓扑不同的相位平面和矢量场图，并提出了该模型的宇宙学解释。
The present paper considers a three-fluid cosmological model consisting of noninteracting dark matter, dark energy and baryonic matter in the background of the Friedmann- Robertson- Walker- Lemaitre flat spacetime. It has been assumed that the dark matter takes the form of dust whereas the dark energy is a quintessence (real) scalar field with exponential potential. It has been further assumed that the baryonic matter is a perfect fluid with barotropic equation of states. The field equations for this model takes the form of an autonomous dynamical system after some suitable changes of variables. Then a complete stability analysis is done considering all possible parameter (the adiabatic index of the baryonic matter and the parameter arising from the dark energy potential) values and for both the cases of hyperbolic and non-hyperbolic critical points. For non-hyperbolic critical points, the invariant manifold theory (center manifold approach) is applied. Finally various topologically different phase planes and vector field diagrams are produced and the cosmological interpretation of this model is presented.
