# EPRL/FK Asymptotics and the Flatness Problem

## TL;DR

This paper investigates the asymptotic behavior of the EPRL/FK spin foam model in quantum gravity, analyzing whether its classical limit accurately reproduces curved spacetimes or is limited to flat geometries, thus addressing the flatness problem.

## Contribution

It provides a practical computation of spin foam data for a simple triangulation and discusses implications for the flatness problem in the EPRL/FK model.

## Key findings

- Results suggest limitations in the model's ability to reproduce curved geometries.
- The study offers insights into the flatness problem and the classical limit of spin foam models.
- Analysis indicates potential constraints on the model's semiclassical behavior.

## Abstract

Spin foam models are an approach to quantum gravity based on the concept of sum over states, which aims to describe quantum spacetime dynamics in a way that its parent framework, loop quantum gravity, has not as of yet succeeded. Since these models' relation to classical Einstein gravity is not explicit, an important test of their viabilitiy is the study of asymptotics - the classical theory should be obtained in a limit where quantum effects are negligible, taken to be the limit of large triangle areas in a triangulated manifold with boundary. In this paper we will briefly introduce the EPRL/FK spin foam model and known results about its asymptotics, proceeding then to describe a practical computation of spin foam and semiclassical geometric data for a simple triangulation with only one interior triangle. The results are used to comment on the "flatness problem" - a hypothesis raised by Bonzom (2009) suggesting that EPRL/FK's classical limit only describes flat geometries in vacuum.