标题： 一种用于探索$f(R)$引力中反弹和循环宇宙演化的模型无关的紧凑动力系统表述 显示英文标题

标题： A model-independent compact dynamical system formulation for exploring bounce and cyclic cosmological evolutions in $f(R)$ gravity

摘要： 使用动力系统方法结合宇宙学参数，我们提出了一个与模型无关的动力系统公式，用于f(R)引力中的宇宙学。 这种公式是与模型无关的，因为不需要事先指定f(R)的具体函数形式，而是需要指定特定的宇宙学演化，这决定了宇宙学参数。 从某种意义上说，我们的方法是重建方法的反向途径。 这一点通过非紧致和紧致的动力变量进行了说明。 本文的重点是紧致分析，因为我们通过反弹宇宙和循环宇宙的例子展示了该公式的适用性。 特别是，我们的分析以与模型无关的方式揭示了当宇宙整体空间平坦且没有物质时实现此类宇宙学的问题。 显示英文摘要

摘要： Using the dynamical systems approach together with the cosmographic parameters, we present a model-independent dynamical system formulation for cosmology in f(R) gravity. The formulation is model-independent in the sense that one needs to specify not a particular functional form of f(R) a-priori, but rather a particular cosmological evolution, which fixes the cosmography. In a sense, our approach is the way around the reconstruction method. This is shown using both non-compact and compact dynamical variables. The focus in this paper is on the compact analysis since we demonstrate the applicability of this formulation using examples of bouncing and cyclic cosmology. In particular, our analysis reveals, in a model-independent manner, the problem of achieving such cosmologies when the universe is globally spatially flat and devoid of matter.