In this paper, we have investigated the phase space analysis in modified Galileon cosmology, where the Galileon term is considered a coupled scalar field, F(ϕ). We focus on the exponential type function of F(ϕ) and the three well-motivated potential functions V(ϕ). We obtain the critical points of the autonomous system, along with their stability conditions and cosmological properties. The critical points of the autonomous system describe different phases of the Universe. The scaling solution for critical points was found in our analysis to determine the matter-dark energy and radiation-dark energy-dominated eras of the Universe. In these scaling solutions, dark energy is typically introduced alongside another component, such as radiation or matter, and helps explain the transition between cosmological eras. The dark energy dominated critical points show stable behavior and indicate the late-time cosmic acceleration phase of the Universe. Further, the results are examined with the Hubble rate H(z) and the Supernovae Ia cosmological data sets.

中文翻译：

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修正伽利略宇宙学中的动力学系统分析


在本文中，我们研究了修正伽利略宇宙学中的相空间分析，其中伽利略项被认为是耦合标量场 F（φ）。我们专注于 F（φ） 的指数型函数和三个良好激发的势函数 V（φ）。我们获得了自主系统的关键点，以及它们的稳定性条件和宇宙学特性。自治系统的关键点描述了宇宙的不同阶段。在我们的分析中发现了临界点的缩放解决方案，以确定宇宙中物质-暗能量和辐射-暗能量占主导地位的时代。在这些缩放解决方案中，暗能量通常与另一种成分（如辐射或物质）一起引入，并有助于解释宇宙学时代之间的过渡。暗能量占主导地位的临界点表现出稳定的行为，并表明宇宙处于宇宙加速阶段的后期。此外，使用哈勃速率 H（z） 和超新星 Ia 宇宙学数据集对结果进行了检查。