Relational and semiclassical aspects of group field theory: from quantum gravity to cosmology

Driven by the ambition and the fundamental need to reconcile quantum theory with general relativity, research in quantum gravity has grown steadily over the decades, with several candidates attacking the problem from different angles.

This thesis explores key aspects of the group field theory (GFT) approach to quantum gravity, a non-perturbative framework centred around background independence and discreteness which considers the familiar spacetime of general relativity as emerging from fundamental quantum geometric elements. After reviewing motivations
and foundations of GFT, the thesis focusses on new research that spans three major themes: anisotropic cosmology, semiclassical states, and relational dynamics.

First, the thesis introduces anisotropic GFT cosmological models, broadening the current understanding beyond isotropic settings by incorporating new anisotropy degrees of freedom from quantum gravity considerations. These results enhance the applicability of GFT to more complex scenarios, which can lead to a variety of new phenomenological applications. Next, a comprehensive semiclassical investigation provides a unified framework of Gaussian states for GFT cosmology, which generalises all previously studied quantum states and properties. Quantum fluctuations are shown to be under control, ensuring that models derived from GFT exhibit a semiclassical behaviour, crucial for bridging quantum gravity with large-scale cosmology. Finally, the thesis addresses a critical conceptual challenge in quantum gravity: relational dynamics as a solution to the problem of time. By means of quantum clocks, the Page–Wootters formalism (here applied for the first time in non-perturbative quantum gravity) yields a covariant formulation of quantum dynamics in GFT. This allows for a coherent framework that relates to established canonical quantisation methods, strengthened by a conditional interpretation.

All such findings help address significant questions in GFT by offering novel phenomenological perspectives for cosmology, an exhaustive semiclassical analysis, and clear insights on the notion of (quantum) covariance. They also suggest many avenues for future research.