Abstract
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.