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arXiv 2103.02715gr-qc
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Dirac-Born-Infeld模型的动力系统分析:中心流形的观点

Dynamical System Analysis of a Dirac-Born-Infeld Model : A Center Manifold Perspective

Subhajyoti Pal, Subenoy Chakraborty

摘要:

在本文中,我们提出了一个理想流体的宇宙动力学和宇宙的暗能量(DE)的组成部分,我们的暗能量模型是弦理论的Dirac Born Infeld(DBI)模型。我们假设DBI模型额外维紧致空间的标量场的势和弯曲喉道区的弯曲因子都是指数性质的。在空间平坦的Friedman-Robertson-Walker-Lemaitre宇宙背景下,DBI暗能量的爱因斯坦场方程可化为一个自治动力学系统.然后,我们对这个系统进行动力系统分析。我们的分析是出于不变流形的数学动力学方法。在这种方法中,即使动力系统的临界点是非双曲的,也有可能得到一个确定的结论。由于我们找到了这个系统的完整的临界点集,中心流形分析确保了我们对这个模型的研究不留任何余地。我们发现了一些有趣的结果,例如,对于某些临界点,存在缩放解的情况。最后,我们提出了各种拓扑不同的相平面和稳定性图,并讨论了相应的宇宙学方案。

英文摘要:

In this paper we present the cosmological dynamics of a perfect fluid and the Dark Energy (DE) component of the Universe, where our model of the dark energy is the string-theoritic Dirac-Born-Infeld (DBI) model. We assume that the potential of the scalar field and the warp factor of the warped throat region of the compact space in the extra dimension for the DBI model are both exponential in nature. In the background of spatially flat Friedman-Robertson-Walker-Lemaitre Universe, the Einstein field equations for the DBI dark energy reduce to a system of autonomous dynamical system. We then perform a dynamical system analysis for this system. Our analysis is motivated by the invariant manifold approach of the mathematical dynamics. In this method, it is possible to reach a definite conclusion even when the critical points of a dynamical system are non-hyperbolic in nature. Since we find the complete set of critical points for this system, the center manifold analysis ensures that our investigation of this model leaves no stone unturned. We find some interesting results such as that for some critical points there are situations where scaling solutions exist. Finally we present various topologically different phase planes and stability diagrams and discuss the corresponding cosmological scenario.

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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