Time evolution of semiclassical states in the one-vertex model of quantum-reduced loop gravity

We compute numerically the time evolution of simple semiclassical states describing homogeneous and isotropic spatial geometries in quantum-reduced loop gravity under a deparametrized formulation of the dynamics, in which a reference matter field is taken as a relational time variable for the dynamics of quantum states of the gravitational field. The states which we consider are defined on the Hilbert space of a spin network graph formed by a single six-valent vertex. We find that the quantum dynamics is generally in close agreement with the semiclassical effective dynamics of a homogeneous and isotropic universe throughout the range of validity of the numerical approximation. In particular, an initial state describing a contracting geometry undergoes a dynamical “bounce”, where the contraction is halted and turned into an expansion by the quantum dynamics.