Exploring the pre-inflationary universe for the family of α-attractor potentials

In the framework of loop quantum cosmology, we investigate the dynamics of pre-inflation with a family of [Formula: see text]attractor potentials. At the quantum bounce, either the kinetic energy or the potential energy of the inflation field dominates the background evolution. We determine the physically feasible initial conditions in both classes that yield the slow-roll inflation and enough number of [Formula: see text]-folds to be consistent with observations. The background evolution before reheating is consistently divided into three distinct phases: bouncing, transition, and slow-roll inflation in the case of kinetic energy dominated evolution at the bounce, while the first two phases disappear in the case of potential energy dominated evolution, though slow-roll inflation is still possible. We also explore the phase space trajectories for physically feasible initial conditions of the inflaton field and study the phase space analysis for a class of [Formula: see text]attractor potentials.