QG1 - Loop Quantum Gravity, Quantum Geometry, Spin Foams |
Speaker |
Dupuis, Maite |
Coauthors |
|
Talk Title |
The cosmological constant in the Loop Quantum Gravity framework. |
Abstract |
The Loop Quantum Gravity framework has been mostly studied in the case of a zero vanishing cosmological constant. A Loop Quantum Gravity model with a cosmological constant is not well understood even in the 3d toy model case. For the 3d case, several approaches to define a model of quantum gravity exist and in the case of a non-vanishing cosmological constant, the models such as the Turaev-Viro spin foam model or the Chern-Simons model are written in terms of a quantum group. To reconcile the Loop Quantum Gravity approach with these models, we deform the Loop Quantum Gravity framework using quantum groups or Poisson-Lie groups. Following this line, a topological model with a Hamiltonian constraint for 3d gravity with a cosmological constant has been defined. The Hamiltonian constraint can be solved and the solutions can be related to the Turaev-Viro spin foam amplitude. Moreover, geometric observables for quantum hyperbolic geometries have been defined. I am going to present an overview of this program consisting in introducing a cosmological constant in the 3d Loop Quantum gravity framework and will comment the 4d case. |
Talk view |
|
|