Emergent cosmology from quantum gravity in the Lorentzian Barrett-Crane tensorial group field theory model

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 SU(2)-based EPRL-like models. Also in this manifestly Lorentzian setting, in which only continuous SL(2, 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.

Automated summary

In this study, we investigate the cosmological sector of the Lorentzian Barrett-Crane model and find that it exhibits homogeneous and isotropic cosmological dynamics similar to the SU(2)-based EPRL model. By using continuous SL(2, C) representations, we derive generalized Friedmann equations that show a quantum bounce and can reproduce all the features of the cosmological dynamics in the EPRL model.