论文标题
在散装粘性宇宙学中退化的Bogdanov-Takens分叉
Degenerate Bogdanov-Takens bifurcations in a bulk viscous cosmology
论文作者
论文摘要
使用动力学系统理论，我们表明，在存在宇宙常数的情况下，具有散装粘性流体的Friedmann-Robertson-Walker（FRW）宇宙学模型等于退化的二维Bogdanov-Takens正常形式。状态参数的方程式，$ω$，批量粘度系数，$ξ$和宇宙常数$λ$，定义了展开退化的bogdanov-takens系统的必要参数。在更改相关参数$ω$，$λ$和$ξ$时，讨论了系统的固定点以及其稳定性属性的变化。通过适当的分叉图可视化稳定性的变化。展示了有限领域和全球阶段肖像的相位肖像，并讨论了结构稳定性的问题。还讨论了典型的问题，例如粘度延迟加速或通货膨胀，并可能与观察性宇宙学相关。
Using the dynamical system theory we show that the Friedmann-Robertson-Walker (FRW) cosmological model with bulk viscous fluid in the presence of cosmological constant is equivalent to a degenerate two dimensional Bogdanov-Takens normal form. The equation of state parameter, $ω$, the bulk viscosity coefficient, $ξ$, and the cosmological constant, $Λ$, define the necessary parameters for unfolding the degenerate Bogdanov-Takens system. The fixed points of the system are discussed together with the variation of their stability properties upon changing the relevant parameters $ω$, $Λ$ and $ξ$. The variation of the stability properties are visualized by the appropriate bifurcation diagrams. Phase portrait for finite domain and global phase portrait are displayed and the issue of the structural stability is discussed. Typical issues such as late acceleration or inflation that can be induced by viscosity and could have relevance to observational cosmology are also discussed.
