# Towards a Cosmological subsector of Spin Foam Quantum Gravity

## TL;DR

This paper analyzes a symmetric, cosmologically relevant sector of the EPRL-FK spin foam model, deriving effective dynamics that recover Friedmann-Robertson-Walker cosmology in the large lattice limit, and sets the stage for renormalization of curved geometries.

## Contribution

It introduces a symmetry-restricted spin foam model that captures cosmological dynamics and provides explicit quantum corrections, advancing the understanding of quantum gravity in cosmological settings.

## Key findings

- Recovered FRW dynamics in large lattice limit
- Derived Regge-type action and quantum corrections
- Analyzed cases with vacuum, cosmological constant, and dust

## Abstract

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. We investigate the action in the three cases of vacuum, a cosmological constant, and coupled to dust, and find that in all cases, the corresponding FRW dynamics is recovered in the limit of large lattices. While this work demonstrates a large intersection with computations done in the context of cosmological modelling with Regge Calculus, it is ultimately a setup for treating curved geometries in the renormalization of the EPRL-FK spin foam model.