Seminarium Teorii Względności i Grawitacji

Quantum-reduced loop gravity is a model of loop quantum gravity, whose simplified kinematical structure makes it possible to explore practical applications which would be very challenging, if not completely intractable to analyze within the framework of the full theory. After giving a brief introduction to the quantum-reduced model and its relation with full loop quantum gravity, we present a proposal for a Hamiltonian constraint operator governing the dynamics of the model. In contrast to Thiemann's well-known construction of the Hamiltonian constraint in loop quantum gravity, the Lorentzian part of our Hamiltonian is given by an operator representing the scalar curvature of the spatial manifold. As a concrete physical application, we study the dynamics generated by the Hamiltonian in a cosmological setting, both at the level of semiclassical effective dynamics, and in terms of numerical simulations of the time evolution of quantum states describing homogeneous and isotropic spatial geometries.