Including topology change in Loop Quantum Gravity with topspin network formalism with application to homogeneous and isotropic cosmology

TL;DR

This paper extends Loop Quantum Gravity using topspin networks to incorporate topology change, demonstrating its effects in toy models and cosmological scenarios, including superpositions and transition probabilities.

Contribution

It introduces a formalism for topology change in Loop Quantum Gravity using topspin networks and applies it to cosmological models, showing how topology can evolve.

Findings

Topology can change due to Hamiltonian constraint action.

Final states can be superpositions of different topologies.

Transition amplitudes between topological states are calculable.

Abstract

We apply topspin network formalism to Loop Quantum Gravity in order to include in the theory the possibility of changes in the topology of spacetime. We apply this formalism to three toy models: with the first, we find that the topology can actually change due to the action of the Hamiltonian constraint and with the second we find that the final state might be a superposition of states with different topologies. In the third and last application, we consider an homogeneous and isotropic Universe, calculating the difference equation that describes the evolution of the system and which are the final topological states after the action of the Hamiltonian constraint. For this last case, we also calculate the transition amplitudes and probabilities from the initial to the final states.