  With a well-motivated extension of higher order holonomy corrections, the
quantum theory of loop quantum cosmology (LQC) for the $k=0$
Friedmann-Robertson-Walker model (with a free massless scalar) is rigorously
formulated. The analytical investigation reveals that, regardless of the order
of holonomy corrections and for any arbitrary states, the matter density
remains finite, bounded from above by an upper bound, which equals the critical
density obtained at the level of heuristic effective dynamics. Particularly,
with all orders of corrections included, the dynamical evolution is shown to
follow the bouncing scenario in which two Wheeler-DeWitt (WDW) solutions
(expanding and contracting) are bridged together through the quantum bounce.
These observations provide further evidence that the quantum bounce is
essentially a consequence of the intrinsic discreteness of LQC and LQC is
fundamentally different from the WDW theory. Meanwhile, the possibility is also
explored that the higher order holonomy corrections can be interpreted as a
result of admitting generic SU(2) representations for the Hamiltonian
constraint operators.
