arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2002.07588gr-qc
收藏

三流体宇宙模型的动力学系统分析:不变流形方法

Dynamical System Analysis of a Three Fluid Cosmological Model : An Invariant Manifold approach

Subhajyoti Pal, Subenoy Chakraborty

摘要:

本文研究了在Friedmann-Robertson- Walker- Lemaitre平坦时空背景下由无相互作用的暗物质、暗能量和重子物质组成的三流体宇宙学模型。暗物质被假定为尘埃的形式,而暗能量是一个具有指数势的经典(实)标量场。进一步假定重子物质是具有正压状态方程的理想流体。该模型的场方程经过适当的变量变换后,可以形成一个自治的动力系统。然后,考虑所有可能的参数(重子物质的绝热指数和由暗能量势引起的参数)值,对双曲和非双曲临界点的情况进行了完整的稳定性分析。对于非双曲临界点,应用不变流形理论(中心流形方法)。最后给出了各种拓扑结构不同的相平面和矢量场图,并给出了该模型的宇宙学解释。

英文摘要:

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.

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。

↑