# Emergent 4-dimensional linearized gravity from spin foam model

## TL;DR

This paper demonstrates that linearized Einstein gravity and smooth curved spacetime geometries can emerge from Spin Foam Models in Loop Quantum Gravity at low energies, supporting the theory's validity.

## Contribution

It shows for the first time that SFMs can produce all solutions of linearized Einstein equations, establishing a link between quantum spin foam models and classical gravity.

## Key findings

- Emergence of smooth curved spacetimes from SFMs
- Linearized Einstein equations satisfied by SFM perturbations
- Deformation parameter introduces higher curvature corrections

## Abstract

Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete SFMs under an appropriate low energy limit, which corresponds to a semiclassical continuum limit of SFMs. In particular, we show that the low energy excitations of SFMs on a flat background give all smooth solutions of linearized Einstein equations (spin-2 gravitons). This indicates that at the linearized level, classical Einstein gravity is indeed the low energy effective theory from SFMs. Thus our result heightens the confidence that covariant LQG is a consistent theory of quantum gravity. As a key technical tool, a regularization/deformation of the SFM is employed in the derivation. The deformation parameter $\delta$ becomes a coupling constant of a higher curvature correction term to Einstein gravity from SFM.