Towards anisotropic cosmology in group field theory

TL;DR

This paper extends group field theory models of quantum gravity to include anisotropic cosmologies, introducing a new anisotropy observable and demonstrating its classical and quantum behavior, paving the way for matter-free relational dynamics.

Contribution

It introduces a novel anisotropy observable in GFT for Bianchi models and analyzes its classical and quantum dynamics, advancing the understanding of anisotropic quantum cosmology.

Findings

The anisotropy variable behaves as a massless scalar in classical Bianchi I spacetime.

In GFT, the anisotropy initially mimics classical behavior and then decays, indicating isotropisation.

Numerical and analytical methods support the proposed dynamics of anisotropy in GFT.

Abstract

In cosmological group field theory (GFT) models for quantum gravity coupled to a massless scalar field the total volume, seen as a function of the scalar field, follows the classical Friedmann dynamics of a flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) Universe at low energies while resolving the Big Bang singularity at high energies. An open question is how to generalise these results to other homogeneous cosmologies. Here we take the first steps towards studying anisotropic Bianchi models in GFT, based on the introduction of a new anisotropy observable analogous to the $\beta$ variables in Misner's parametrisation. In a classical Bianchi I spacetime, $\beta$ behaves as a massless scalar field and can be used as a (gravitational) relational clock. We construct a GFT model for which in an expanding Universe $\beta$ initially behaves like its classical analogue before "decaying" showing a previously studied isotropisation. We support numerical results in GFT by analytical approximations in a toy model. One possible outcome of our work is a definition of relational dynamics in GFT that does not require matter.