# Bouncing evolution in a model of loop quantum gravity

## TL;DR

This paper investigates a simplified loop quantum gravity model with a single-vertex graph, revealing a bouncing evolution that echoes the quantum bounce in loop quantum cosmology, linking singularity resolution to quantum geometry.

## Contribution

It introduces a graph-preserving Hamiltonian in a simplified loop quantum gravity model and demonstrates bouncing dynamics, connecting full theory insights to cosmological quantum bounces.

## Key findings

- Bouncing evolution observed in the model.
- Explicit matrix elements of the Hamiltonian derived.
- Connection established between quantum bounce and quantum geometry.

## Abstract

To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex. The Hamiltonian operator $\hat{H}_v$ is chosen to be graph-preserving, and the matrix elements of $\hat{H}_v$ are explicitly worked out in a suitable basis. The non-trivial Euclidean part $\hat{H}_v^E$ of $\hat{H}_v$ is studied in details. It turns out that by choosing a specific symmetrization of $\hat{H}_v^E$, the dynamics driven by the Hamiltonian gives a picture of bouncing evolution. Our result in the model of full loop quantum gravity gives a significant echo of the well-known quantum bounce in the symmetry-reduced model of loop quantum cosmology, which indicates a closed relation between singularity resolution and quantum geometry.