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arXiv 2003.10915gr-qc
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具有高斯势的薄膜上的精粹场薄膜诱导引力的稳定性分析

The Stability Analysis of Brane Induced Gravity with Quintessence Field on the Brane with a Gaussian Potential

Arvin Ravanpak, Golnaz Farpour Fadakar

摘要:

本文考虑DGP宇宙学模型的一个正规分支,其中膜上有一个精粹标量场作为暗能量分量。利用动力系统方法,我们研究了该模型的稳定性。我们发现,λ作为一个新的无量纲变量,在宇宙历史中起着至关重要的作用。我们将讨论分为两部分:常数λ和变化λ。在λ为常数的情况下,我们计算了模型的所有临界点,甚至是无穷远处的临界点,然后假设它们都是变λ情况下的瞬时临界点,这是本文的主要部分。我们发现在这样的模型中额外维数的影响与λ的值无关。然后,我们考虑高斯势,其中λ不是常数,而是从零到无穷大变化。我们讨论了该模型的动力学变量的演化,并得出结论,他们的渐近行为遵循的运动临界点的轨迹。同时,我们发现宇宙有两种可能的命运。在其中一种情况下,它可能会经历加速膨胀,但随后进入减速阶段,最终达到稳定的物质主导解决方案。在另一种情况下,宇宙可以接近物质主导的临界点,而不经历任何加速膨胀。我们认为,第一种情况更符合观察。

英文摘要:

In this paper, we consider a normal branch of the DGP cosmological model with a quintessence scalar field on the brane as the dark energy component. Using the dynamical system approach, we study the stability properties of the model. We find that λ, as one of our new dimensionless variables which is defined in terms of the quintessence potential, has a crucial role in the history of the universe. We divide our discussion into two parts: a constant λ and a varying λ. In the case of a constant λ, we calculate all the critical points of the model even those at infinity and then assume all of them as instantaneous critical points in the varying λ situation which is the main part of this paper. We find that the effect of the extra dimension in such a model is independent of the value of λ. Then, we consider a Gaussian potential for which λ is not constant but varies from zero to infinity. We discuss the evolution of the dynamical variables of the model and conclude that their asymptotic behaviors follow the trajectories of the moving critical points. Also, we find two different possible fates for the universe. In one of them, it could experience an accelerated expansion, but then enters a decelerating phase and finally reaches a stable matter-dominated solution. In the other scenario, the universe could approach the matter-dominated critical point without experiencing any accelerated expansion. We argue that the first scenario is more compatible with observations.

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