Quantum Reduced Loop Gravity: Semiclassical limit

Abstract

We discuss the semiclassical limit of Quantum Reduced Loop Gravity, a recently proposed model to address the quantum dynamics of the early Universe. We apply the techniques developed in full Loop Quantum Gravity to define the semiclassical states in the kinematical Hilbert space and evaluating the expectation value of the euclidean scalar constraint we demonstrate that it coincides with the classical expression, {\it i.e.} the one of a local Bianchi I dynamics. The result holds as a leading order expansion in the scale factors of the Universe and opens the way to study the subleading corrections to the semiclassical dynamics. We outline how by retaining a suitable finite coordinate length for holonomies our effective Hamiltonian at the leading order coincides with the one expected from LQC. This result is an important step in fixing the correspondence between LQG and LQC.