Many-nodes/many-links spinfoam: the homogeneous and isotropic case

Understand

I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry.

• This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the compete graph on 5 nodes.
• All the resulting amplitudes have the same support, independently of the graph used, in the large j (large volume) limit.
• This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant.