Effect of the Inverse Volume Modification in Loop Quantum Cosmology

Abstract

It is known that in loop quantum cosmology (LQC) the universe avoids the singularity by a bounce when the matter density approaches the critical density $\rho_c$ (the order of Planck density). After incorporating the inverse volume modifications both in the gravitational and matter part in the improved framework of LQC, we find that the inverse volume modification can decrease the bouncing energy scale, and the presence of nonsingular bounce is generic. For the backward evolution in the expanding branch, in terms of different initial states the evolution trajectories classify into two classes. One class with larger initial energy density leads to the occurrence of bounce in the region $a>a_{ch}$ where $a_{ch}$ marks the different inverse volume modification region. The other class with smaller initial energy density evolves back into the region $a<a_{ch}$. In this region, both the energy density for the scalar field and the bouncing energy scale decrease with the backward evolution. However, in the deep modification region, because of the inverse volume modification the scalar field is frozen, such that the bounce is present when the bouncing energy scale decreases to be equal to the energy density of the scalar field. Using numerical method, we show the evolution picture for the second class bounce.