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Coherent state functional integral for the minisuperspace model of loopquantum cosmology is studied. By the well-established canonical theory, thetransition amplitude in the path integral representation of loop quantumcosmology with alternative dynamics can be formulated through group averaging.The effective action and Hamiltonian with higher-order quantum corrections arethus obtained. It turns out that for a non-symmetric Hamiltonian constraintoperator, the Moyal (star)-product emerges naturally in the effectiveHamiltonian. For the corresponding symmetric Hamiltonian operator, the resultedeffective theory implies a possible quantum cosmological effect in large scalelimit in the alternative dynamical scenario, which coincides with the result incanonical approach. Moreover, the first-order modified Friedmann equation stillcontains the particular information of alternative dynamics and hence admitsthe possible phenomenological distinction between the different proposals ofquantum dynamics.

Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics