High-performance computing in covariant Loop Quantum Gravity
Abstract
This Ph.D. thesis presents a compilation of the scientific papers I published over the last three years during my Ph.D. in loop quantum gravity (LQG). First, we comprehensively introduce spinfoam calculations with a practical pedagogical paper. We highlight LQG's unique features and mathematical formalism and emphasize the computational complexities associated with its calculations. The subsequent articles delve into specific aspects of employing high-performance computing (HPC) in LQG research. We discuss the results obtained by applying numerical methods to studying spinfoams' infrared divergences, or ``bubbles''. This research direction is crucial to define the continuum limit of LQG properly. We investigate the self-energy diagram in LQG, analyzing the scaling of the divergence of the associated amplitude. Using the same technique, we compute the spinfoam amplitudes of a class of two-vertex diagrams. Besides divergent graphs, our investigations yield striking and surprising numerical evidence that spinfoam-containing bubbles can have finite transition amplitudes. Furthermore, we adapt Monte Carlo methods to the spinfoam formalism. We employ this technique to analyze the vertex renormalization amplitude. We find numerical solid indications that this amplitude is convergent, opening new perspectives for renormalizing large-volume infrared spinfoam bubbles. In spinfoam cosmology, we investigate the integration of HPC with Markov Chain Monte Carlo simulations, proving the potential to analyze the macroscopic properties of quantum spacetime. We perform a spinfoam refinement process starting from the simplest diagram, demonstrating the effectiveness of this hybrid approach and elucidating the connection of LQG observables with spacetime geometry. Furthermore, we apply the same technique to investigate the spinfoam with a 16-cell boundary using a topological model. Finally, we outline a numerical algorithm to compute the transition amplitude from a black hole to a ``white hole''. The recently proposed hypothetical decay process via gravitational quantum tunneling is one of the most intriguing hypotheses on the future of black holes. We use the spinfoam approach and HPC to investigate this phenomenon by explicitly computing the associated transition amplitude. The advancements of HPC-assisted LQG research will hopefully enable the study of complex gravitational phenomena at unprecedented scales, paving the way for exploring previously inaccessible physical regimes.