Towards a Cosmological subsector of Spin Foam Quantum Gravity

Understand

We examine the four dimensional path integral for Euclidean quantum gravity in the context of the EPRL-FK spin foam model.

• The state sum is restricted to certain symmetric configurations which resembles the geometry of a flat homogeneous and isotropic universe.
• The vertex structure is specially chosen so that a basic concept of expansion and contraction of the lattice universe is allowed.
• We compute the asymptotic form of the spin foam state sum in the symmetry restricted setting, and recover a Regge-type action, as well as an explicit form of the Hessian matrix, which captures quantum corrections.