论文标题
约束$ f（r）$重力模型与延迟宇宙学的演变
Constraining $f(R)$ Gravity Models with The Late-Time Cosmological Evolution
论文作者
论文摘要
$ f（r）$修改的重力是爱因斯坦一般相对论的一种修改，该理论旨在解释超出宇宙学标准模型（例如暗能量和暗物质）的问题。作为在宇宙大规模的重大动态的重力理论，$ f（r）$模型应该能够解释从以物质主导的宇宙向黑暗能源为主的宇宙的过渡。假设可以在从物质主导的宇宙到黑暗能力主导的宇宙的过渡过程中忽略辐射的密度参数，我们发现有关模型密度参数的动力学稳定性的一些固定点。如果$ f（r）$模型可以将固定点$ p_5 $（代表物质主导的时代）连接到固定点$ p_1 $（代表黑暗能源主导的时代），则可以实现相变。评估该状态过渡的方法称为定点分析。在这项研究中，我们分析了Starobinsky，Hu-Sawicki和Gogoi-Goswami提出的$ f（r）$模型的生存能力，内容涉及从物质主导的宇宙到黑暗能量主导的宇宙的相变。结果表明，这些模型可以通过选择一些适当的参数来可行。例如，在Starobinsky和Hu-Sawicki型号中，可以选择参数$μ$以对应于$ x_d = r_1/rc $的下限，其中$ r_1 $代表de-sitter点。同时，对于Gogoi-Guswami模型，可以通过服用$α$和$β$参数来满足De-Sitter点的存在和稳定性条件，从而实现相同的结果。从这些结果可以得出的结论是，这些$ f（r）$模型允许宇宙的这种阶段过渡实现延迟加速的扩张。
The $f(R)$ Modified Gravity is a modification of Einstein's general theory of relativity, which aims to explain issues beyond The Standard Model of Cosmology such as dark energy and dark matter. As a theory of gravitation that govern major dynamics on the large scale of the universe, an $ f(R)$ model should be able to explain the transition from a matter-dominated universe to a dark-energy-dominated universe. Assuming that the density parameter of the radiation can be neglected during the transition from a matter-dominated universe to a dark-energy-dominated universe, we find some fixed points regarding the dynamical stability of the density parameters of the model. The phase transition can be achieved if the $f(R)$ model can connect the fixed point $P_5$ (representing the matter-dominated era) to the fixed point $P_1$ (representing the dark energy-dominated era). The method to evaluate that state transition is called the Fixed-point analysis. In this study, we analyze the viability of $f(R)$ models proposed by Starobinsky, Hu-Sawicki, and Gogoi-Goswami regarding the phase transition from a matter-dominated universe to a dark-energy-dominated universe. It is shown that those models are viable by choosing some set of appropriate parameters. For example, in the Starobinsky and Hu-Sawicki models, the parameter $μ$ can be chosen to correspond to the lower bound of $x_d= R_1/Rc$, where $R_1$ represents the de-Sitter point. Meanwhile, for the Gogoi-Guswami model, the same results can be achieved by taking $α$ and $β$ parameters satisfying the existence and stability conditions for the de-Sitter point. From these results, it can be concluded that those $f(R)$ models allow such phase transitions of the universe to realize the late-time accelerated expansion.
