Initial Conditions of Inflaton Field at the Quantum Bounce

In this paper, we explore the pre-inflationary evolution of the universe driven by a logarithmic potential in the context of Loop Quantum Cosmology. Our analysis focuses on identifying the physically admissible initial conditions for the inflaton field that result in a successful phase of slow-roll inflation. We also evaluate the corresponding number of e-folds and examine their consistency with current observational bounds. When the kinetic energy of the inflaton dominates at the initial stage, the cosmic evolution prior to reheating naturally separates into three successive phases: the bouncing phase, the transition phase, and the slow-roll inflationary phase. Throughout the bouncing phase, the dynamics of the scale factor are largely insensitive to both the chosen initial conditions and the detailed structure of the inflationary potential. In this regime, the evolution admits an explicit analytical solution, providing a clear and model-independent description of the background behavior before the onset of inflation. In this model, the quantum bounce is governed entirely by kinetic energy, since potential energy dominated initial conditions cannot be realized over the full range of inflaton field.