Gravitação quântica de laços e cosmologia spinfoam - Gabriel Batista Vilaça (2024)
One of the biggest challenges in theoretical physics is the construction of a quantum theory of gravity. One of the most promising candidates is Loop Quantum Gravity, a non-perturbative, background independent quantum theory of General Relativity. One of the goals of this dissertation is to construct the theory of Loop Quantum Gravity, following the spinfoam approach, which starts from the Lagragian formalism of General Relativity and uses quantization techniques inspired by lattice gauge theories, based on a discretization of spacetime. As main results, we have the construction of the spin-network basis, the area and volume operators, which have a discrete spectrum, and the EPRL/FK vertex, which implents the dynamics. In order to test the predictions of the theory, one of the areas of greatest interest is Cosmology. Another objective of this dissertation is to show a way to implement the cosmological limit starting from the complete theory, using coherent states of Loop Quantum Gravity picked around homogeneous and isotropic geometries and studying the dynamics in first order. As a main result, we show that the transition amplitudes returns the classical limit expected by Cosmology.