Speaker
Description
We study the quantum dynamics of a simple class of states in quantum-reduced loop gravity. These states are based on a cubic graph consisting of a single six-valent vertex. The dynamics is governed by a Hamiltonian constraint operator, whose Lorentzian part is represented by the scalar curvature operator introduced by Jurek and myself a couple of years ago. We observe a certain formal similarity between the Euclidean part of the Hamiltonian acting on the single-vertex states, and the Hamiltonian constraint of anisotropic Bianchi I models in loop quantum cosmology. By extending this formal analogy to the Lorentzian part of the Hamiltonian, we are led to suggest a possible modified definition of the Hamiltonian constraint for loop quantum cosmology, in which the Lorentzian part (corresponding to the scalar curvature of the spatial manifold) is not assumed to be identically vanishing and is represented by a non-trivial quantum operator.
