  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.
