  The loop quantum cosmological model from ADM Hamiltonian is studied in this
paper. We consider the spatially flat homogeneous FRW model. It turns out that
the modified Friedmann equation keeps the same form as the APS LQC model.
However, the critical matter density for the bounce point is only a quarter of
the previous APS model, i.e. $\rho_{cL}=\frac{\rho_c}{4}$. This is interesting
because the lower critical bounce density means the quantum gravity effects
will get involved earlier than the previous LQC model. Besides, the lower
critical density also means the detection of quantum gravity effects easier
than the previous model.
