Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model

TL;DR

This paper investigates the cosmological implications of the Lorentzian Barrett-Crane tensorial group field theory model, demonstrating that it produces effective bouncing cosmologies similar to other quantum gravity models, suggesting a universal quantum gravity mechanism.

Contribution

It extends the study of quantum cosmology to the Lorentzian Barrett-Crane GFT model, showing it yields effective dynamics with quantum bounces comparable to EPRL-like models.

Findings

Generalized Friedmann equations with quantum bounce

Reproduction of cosmological features of EPRL-like models

Support for universality class of quantum gravity mechanisms

Abstract

We study the cosmological sector of the Lorentzian Barrett-Crane (BC) model coupled to a free massless scalar field in its Group Field Theory (GFT) formulation, corresponding to the mean-field hydrodynamics obtained from coherent condensate states. The relational evolution of the condensate with respect to the scalar field yields effective dynamics of homogeneous and isotropic cosmologies, similar to those previously obtained in $\text{SU}(2)$-based EPRL-like models. Also in this manifestly Lorentzian setting, in which only continuous $\text{SL}(2,\mathbb{C})$-representations are used, we obtain generalized Friedmann equations that generically exhibit a quantum bounce, and can reproduce all of the features of the cosmological dynamics of EPRL-like models. This lends support to the expectation that the EPRL-like and BC models may lie in the same continuum universality class, and that the quantum gravity mechanism producing effective bouncing scenarios may not depend directly on the discretization of geometric observables.