Preinflationary Dynamics of Power-Law Potential in Loop Quantum Cosmology †

In this article, I mainly discuss the dynamics of the pre-inflationary Universe for the potential V ( ϕ ) ∝ ϕ n with n = 5 / 3 in the context of loop quantum cosmology, in which the big bang singularity is resolved by a non-singular quantum bounce. In the case of the kinetic energy-dominated initial conditions of the scalar field at the bounce, the numerical evolution of the Universe can be split up into three regimes: bouncing, transition, and slow-roll inflation. In the bouncing regime, the numerical evolution of the scale factor does not depend on a wide range of initial values, or on the inflationary potentials. I calculate the number of e-folds in the slow-roll regime, by which observationally identified initial conditions are obtained. Additionally, I display the phase portrait for the model under consideration