Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology

Abstract

The alternative dynamics of loop quantum cosmology is examined by the path\nintegral formulation. We consider the spatially flat FRW models with a massless\nscalar field, where the alternative quantization inherit more features from\nfull loop quantum gravity. The path integrals can be formulated in both\ntimeless and deparameterized frameworks. It turns out that the effective\nHamiltonians derived from the two different viewpoints are equivalent to each\nother. Moreover, the first-order modified Friedmann equations are derived and\npredict quantum bounces for contracting universe, which coincide with those\nobtained in canonical theory.\n