论文标题
宇宙学模型的动力系统，用于$ g $和$ρ_λ$的不同可能性
Dynamical systems of cosmological models for different possibilities of $G$ and $ρ_Λ$
论文作者
论文摘要
本文介绍了空间平坦的Friedmann-Lemaitre-Robertson-Walker（FLRW）宇宙学模型的动力学，其时间变化了宇宙学常数$λ$，其中$λ$通过Hubble参数（H）随宇宙时间（T）演变而来。我们认为，模型动力学具有反射对称性$ h \ rightarrow -h $，$λ（h）$以泰勒系列的形式相对于H.动力学系统的三种不同情况，基于重力常数g和真空能量密度$ρ_λ$的可能性。如果I，G和$ρ_λ$都被认为是恒定的。我们通过使用光谱半径的概念，沿每个轴沿宇宙时间和繁殖球的扰动的行为来分析系统的稳定性。在情况II中，我们对G =常数和$ρ_λ\ neq $常数具有动态系统分析，在其中使用光谱半径和扰动函数来研究稳定性。在情况III中，我们采用$ g \ \ neq $常数和$ρ_λ\ neq $常数，其中我们引入了一组新的变量来设置相应的动力系统。我们发现系统的固定点并分析了不同方向的稳定性：通过分析沿每个轴的扰动的行为，分别使用Poincare Sphere分别使用Poincare Sphere，中心歧管理论和稳定性。已经提出了相图和扰动图。我们就获得的固定点进行了深入研究，并分析了宇宙的晚期行为。我们的模型同意宇宙处于加速扩张时期。 EOS参数$ω_{eff} $，总能量密度$ω_{tt} $在三种情况的固定点也进行了评估，这些值与[1]中的观察值一致。
The present paper deals with the dynamics of spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model with a time varying cosmological constant $Λ$ where $Λ$ evolves with the cosmic time (t) through the Hubble parameter (H). We consider that the model dynamics has a reflection symmetry $H \rightarrow -H $ with $Λ(H)$ expressed in the form of Taylor series with respect to H. Dynamical systems for three different cases based on the possibilities of gravitational constant G and the vacuum energy density $ρ_Λ$ have been analysed. In Case I, both G and $ρ_Λ$ are taken to be constant. We analyse stability of the system by using the notion of spectral radius, behavior of perturbation along each of the axis with respect to cosmic time and Poincare sphere. In Case II, we have dynamical system analysis for G=constant and $ρ_Λ \neq $ constant where we study stability by using the concept of spectral radius and perturbation function. In Case III, we take $G \neq$ constant and $ρ_Λ \neq$ constant where we introduce a new set of variables to set up the corresponding dynamical system. We find out the fixed points of the system and analyse the stability from different directions: by analysing behaviour of the perturbation along each of the axis, Center Manifold Theory and stability at infinity using Poincare sphere respectively. Phase plots and perturbation plots have been presented. We deeply study the cosmological scenario with respect to the fixed points obtained and analyse the late time behavior of the Universe. Our model agrees with the fact that the Universe is in the epoch of accelerated expansion. The EOS parameter $ω_{eff}$, total energy density $Ω_{tt}$ are also evaluated at the fixed points for each of the three cases and these values are in agreement with the observational values in [1].
