Group field theory and its cosmology in a matter reference frame

TL;DR

This paper explores how matter reference frames can be integrated into group field theory to better understand emergent spacetime and cosmology, including potential insights into black hole horizons.

Contribution

It introduces a method to incorporate matter reference frames into group field theory, enabling the extraction of physical predictions in quantum gravity models.

Findings

Reproduction of near-horizon Schwarzschild geometry

Application to homogeneous and inhomogeneous cosmology

Proposal of matter coordinates in quantum gravity

Abstract

While the equations of general relativity take the same form in any coordinate system, choosing a suitable set of coordinates is essential in any practical application. This poses a challenge in background-independent quantum gravity, where coordinates are not a priori available and need to be reconstructed from physical degrees of freedom. We review the general idea of coupling free scalar fields to gravity and using these scalars as a "matter reference frame." The resulting coordinate system is harmonic, i.e. it satisfies harmonic (de Donder) gauge. We then show how to introduce such matter reference frames in the group field theory approach to quantum gravity, where spacetime is emergent from a "condensate" of fundamental quantum degrees of freedom of geometry, and how to use matter coordinates to extract physics. We review recent results in homogeneous and inhomogeneous cosmology, and give a new application to the case of spherical symmetry. We find tentative evidence that spherically symmetric group field theory condensates defined in this setting can reproduce the near-horizon geometry of a Schwarzschild black hole.