A qualitative approach to semi-classical loop quantum cosmology

Recently a mechanism was found which allows avoidance of the cosmological singularity within the semi-classical formulation of loop quantum gravity. Numerical studies show that the presence of a self-interaction potential of the scalar field allows the generation of initial conditions for successful slow-roll inflation. In this paper, qualitative analysis of a dynamical system corresponding to the cosmological equations of loop quantum gravity is performed. The conclusion of singularity avoidance in positively curved cosmological models is confirmed. Two cases are considered: massless (with flat potential) and massive scalar fields. An explanation of the initial conditions generation for inflation in models with a massive scalar field is given. The bounce is discussed for models with zero spatial curvature and negative potentials.