In this paper, we study the main cosmological properties of the classical Friedmann equations in the case of homogeneous and isotropic Friedmann–Robertson–Walker Universe and we also generalized the expression of the Friedmann equation in the case of Loop Quantum Cosmology (LQC). Considering the [Formula: see text]-model, we found the solutions of the equations considered for two particular cases, i.e. [Formula: see text] (i.e. the de Sitter solution) and [Formula: see text]. Moreover, we considered and studied two exact cosmological solutions of the [Formula: see text]-model, in particular the power-law and the exponential ones. Moreover, we also considered a third more complicated case and we derived the solution for an arbitrary function of the time [Formula: see text]. A scalar field description of the model is presented by constructing its self-interacting potential.

中文翻译：

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LQG 广义模型的宇宙学

在本文中，我们研究了经典弗里德曼方程在均匀和各向同性弗里德曼-罗伯逊-沃克宇宙的情况下的主要宇宙学性质，并在环量子宇宙学（LQC）的情况下推广了弗里德曼方程的表达式。考虑[公式：见文本]模型，我们找到了两个特定情况下考虑的方程的解，即[公式：见文本]（即德西特解）和[公式：见文本]。此外，我们考虑并研究了 [公式：见正文] 模型的两个精确宇宙学解，特别是幂律和指数解。此外，我们还考虑了第三种更复杂的情况，我们得出了任意时间函数的解[公式：见正文]。