The quantum creation of universes with compactified internal dimensions

Quantum cosmology seeks to provide a quantum-mechanical description of the origin of the Universe by extending the principles of quantum theory to gravitation. Within this framework, the Lorentzian path integral formulation and the no-boundary proposal offer a well-defined prescription for the quantum state of the Universe and its semiclassical emergence. In this thesis, we review the theoretical foundations of Lorentzian quantum cosmology, including the role of Picard-Lefschetz theory, boundary conditions, and the relation between the path integral and the Wheeler-DeWitt equation. We then develop a numerical implementation of complex no-boundary saddle points in minisuperspace and reproduce the semiclassical probability distribution for inflationary histories. Building upon this framework, we extend the analysis to higher-dimensional effective theories containing compactified internal dimensions, with emphasis on uplifted Freund-Rubin radion potentials and Large Volume Scenario scalar potentials. We investigate the existence of regular no-boundary saddle points and compute their corresponding probabilities, showing how the structure of the scalar potential influences the quantum emergence of inflationary universes. Our main result is that, in both models, the no-boundary wave function systematically favours radion configurations away from the flux-stabilized minimum, corresponding to unstable moduli values at which the four-dimensional effective field theory breaks down and the full higher-dimensional gravitational dynamics become relevant. This suggests that moduli stabilization may not be a generic outcome of the quantum initial conditions of the Universe, but rather a subsequent dynamical process. These results show that Lorentzian no-boundary cosmology naturally extends to higher-dimensional, phenomenologically motivated theories, offering a novel probabilistic criterion for vacuum selection and compactification within the landscape of effective theories.