Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime

We study the renormalization group flow of the Euclidean Engle-Pereira-Rovelli-Livine and Freidel-Krasnov (EPRL-FK) spin foam model in the large-j limit. The vertex amplitude is deformed to include a cosmological constant term. The state sum is reduced to describe a foliated spacetime whose spatial slices are flat, isotropic, and homogeneous. The model admits a nonvanishing extrinsic curvature, whereas the scale factor can expand or contract at successive time steps. The reduction of degrees of freedom allows a numerical evaluation of certain geometric observables on coarser and finer discretizations. Their comparison defines the renormalization group (RG) flow of the model in the parameters (alpha, Lambda, G). We first consider the projection of the RG flow along the a direction, which shows a UV-attractive fixed point. Then, we extend our analysis to two- and three-dimensional parameter spaces. Most notably, we find the indications of a fixed point in the (alpha, Lambda, G) space, showing one repulsive and two attractive directions.