  In this paper we construct the Hamiltonian constraint operator of loop
quantum cosmology using holonomies defined for arbitrary irreducible SU(2)
representations labeled by spin J. We show that modifications to the effective
semi-classical equations of motion arise both in the gravitational part of the
constraint as well as matter terms. The modifications are important for
phenomenological investigations of the cosmological imprints of loop quantum
cosmology. We discuss the implications for the early universe evolution.
