Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations

Understand

We develop the "triangulated" version of loop quantum cosmology, recently introduced in the literature.

• We focus on the "dipole" cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra.
• We show that the discrete fiducial connection has a simple and appealing geometrical interpretation and we correct the ansatz on the relation between the model variables and the Friedmann-Robertson-Walker scale factor.
• The modified ansatz leads to the convergence of the Hamiltonian constraint to the continuum one.