  An one-parameter regularization freedom of the Hamiltonian constraint for
loop quantum gravity is analyzed. The corresponding spatially flat, homogenous
and isotropic model includes the two well-known models of loop quantum
cosmology as special cases. The quantum bounce nature is tenable in the
generalized cases. For positive value of the regularization parameter, the
effective Hamiltonian leads to an asymptotic de-Sitter branch of the Universe
connecting to the standard Friedmann branch by the quantum bounce. Remarkably,
by suitably choosing the value of the regularization parameter, the
observational cosmological constant can emerge at large volume limit from the
effect of quantum gravity, and the effective Newtonian constant satisfies the
experimental restrictions in the meantime.
