论文标题
对Hu-Sawicki $ f（R）$暗能量模型（包括空间曲率）的紧凑相位空间的全面分析
A comprehensive analysis of the compact phase space for Hu-Sawicki $f(R)$ dark energy models including spatial curvature
论文作者
论文摘要
我们介绍了Hu-Sawicki $ F（R）$ Dark Energy模型的均质和各向同性Friedmann-Laîmatre-Robertson-Walker宇宙学的全面动力学系统分析。对于通用的$ f（r）$理论，我们概述了相位空间的紧凑过程，通常是4维。我们还概述了如何在$ f（r）$模型的情况下确定对应于当今宇宙的相位空间点的坐标，以及代表$λ$ CDM Evolution历史记录的相空间中的表面方程。接下来，我们将这些程序应用于正在考虑的Hu-Sawicki模型中。我们确定了模型相位空间的一些新颖特征，例如不变的亚曼福尔德的存在和固定点的二维表。我们确定相位空间的物理可行区域，固定点与可能的物质相对应，并讨论了非单明一向的弹跳，重新爆发和循环进化的可能性。我们还提供了比较$λ$ CDM演化和Hu-Sawicki进化的数值分析。
We present a comprehensive dynamical systems analysis of homogeneous and isotropic Friedmann-Laîmatre-Robertson-Walker cosmologies in the Hu-Sawicki $f(R)$ dark energy model for the parameter choice $\{n,C_1\}=\{1,1\}$. For a generic $f(R)$ theory, we outline the procedures of compactification of the phase space, which in general is 4-dimensional. We also outline how, given an $f(R)$ model, one can determine the coordinate of the phase space point that corresponds to the present day universe and the equation of a surface in the phase space that represents the $Λ$CDM evolution history. Next, we apply these procedures to the Hu-Sawicki model under consideration. We identify some novel features of the phase space of the model such as the existence of invariant submanifolds and 2-dimensional sheets of fixed points. We determine the physically viable region of the phase space, the fixed point corresponding to possible matter dominated epochs and discuss the possibility of a non-singular bounce, re-collapse and cyclic evolution. We also provide a numerical analysis comparing the $Λ$CDM evolution and the Hu-Sawicki evolution.
