Covariant loop quantum gravity, commonly referred to as the spinfoam model, provides a regularization for the path integral formalism of quantum gravity. A 4-dimensional Lorentzian spinfoam model with a non-zero cosmological constant has been developed based on quantum SL(2,C) Chern-Simons theory on a graph-complement three-manifold, combined with loop quantum gravity techniques. In this talk, I will give an overview of this spinfoam model and highlight its inviting properties, namely (1) that it yields finite spinfoam amplitude for any spinfoam graph, (2) that it is consistent with general relativity with a non-zero cosmological constant at its classical regime and (3) that there exists a concrete, feasible and computable framework to calculate physical quantities and quantum corrections through stationary phase analysis. I will also discuss recent advancements in this spinfoam model and explore its potential applications.
Laurent Freidel, Joshua Kirklin