Relational evolution of effectively interacting GFT quantum gravity condensates

TL;DR

This paper investigates how effective interactions influence the evolution of GFT condensates, showing classicalization, potential inflationary phases, and rapid isotropization, thereby advancing the understanding of quantum geometry dynamics in GFT cosmology.

Contribution

It introduces the analysis of effective interactions in GFT condensates, including anisotropic configurations and inflationary regimes, extending previous models to more realistic quantum cosmology scenarios.

Findings

Free condensates settle into low-spin configurations.

Volume exhibits accelerated, exponential growth.

Anisotropic systems tend to isotropize quickly.

Abstract

We study the impact of effective interactions onto relationally evolving GFT condensates based on real-valued fields. In a first step we show that a free condensate configuration in an isotropic restriction settles dynamically into a low-spin configuration of the quantum geometry. This goes hand in hand with the accelerated and exponential expansion of its volume, as well as the vanishing of its relative uncertainty which suggests the classicalization of the quantum geometry. The dynamics of the emergent space can then be given in terms of the classical Friedmann equations. In contrast to models based on complex-valued fields, solutions avoiding the singularity problem can only be found if the initial conditions are appropriately chosen. We then turn to the analysis of the influence of effective interactions on the dynamics by studying in particular the Thomas-Fermi regime. In this context, at the cost of fine-tuning, an epoch of inflationary expansion of quantum geometric origin can be implemented. Finally, and for the first time, we study anisotropic GFT condensate configurations and show that such systems tend to isotropize quickly as the value of the relational clock grows. This paves the way to a more systematic investigation of anisotropies in the context of GFT condensate cosmology.