Doctor of Philosophy
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.
Summary for Lay Audience
Loop quantum gravity is a quantum theory of gravity that offers a promising and compelling framework for understanding the fundamental nature of spacetime. We need a complete non-perturbative description of quantum gravity as we still do not know what happens in certain universe regions, such as objects that fall into black holes. At the same time, we need such a theory to reconstruct the early primordial instants of the universe. We must consider general relativity and quantum mechanics together to describe these physical scenarios. LQG is one of the most successful attempts to consistently incorporate such theories into a cohesive framework. It aims to describe the quantum behavior of the gravitational field rather than being a ``theory of everything''. It can be approached using two different formalisms: canonical and covariant. The covariant route, usually called the ``spinfoam'' approach to LQG, is a concrete framework where numerical and analytical calculations of transition amplitudes are possible. My contributions have mainly focused on developing new high-performance computing (HPC) methods relying on spinfoam formalism. Calculations in such a framework are pretty complex, and leveraging the capabilities of HPC systems becomes essential to overcome these challenges and facilitate groundbreaking investigations. Extensive research has been conducted, and this thesis aims to provide a cohesive overview of the advancements and future directions. The potential for HPC-assisted LQG offers new avenues for astrophysics, cosmology, and quantum gravity phenomenology. In summary, this collection of articles demonstrates the role of numerical methods in pushing the boundaries of LQG research.
Frisoni, Pietropaolo, "High-performance computing in covariant Loop Quantum Gravity" (2023). Electronic Thesis and Dissertation Repository. 9815.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Available for download on Sunday, April 14, 2024
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