  The alternative dynamics of loop quantum cosmology is examined by the path
integral formulation. We consider the spatially flat FRW models with a massless
scalar field, where the alternative quantization inherit more features from
full loop quantum gravity. The path integrals can be formulated in both
timeless and deparameterized frameworks. It turns out that the effective
Hamiltonians derived from the two different viewpoints are equivalent to each
other. Moreover, the first-order modified Friedmann equations are derived and
predict quantum bounces for contracting universe, which coincide with those
obtained in canonical theory.
