Ramírez Romero, CupatitzioGarcía Compéan, Héctor HugoRamírez Romero, Cupatitzio; 0000-0001-9864-010XHernández Aguilar, Jorge2026-07-102026-07-102026-01-27https://hdl.handle.net/20.500.12371/33404"In this thesis we present a rigorous examination of vacuum transition probabilities between two minima of a scalar field potential within the framework of quantum cosmology, employing a Lorentzian formalism. The research explicitly incorporates quantum corrections through a Wentzel-KramersBrillouin (WKB) approximation to the Wheeler-DeWitt equation, extending the analysis to General Relativity in (2 + 1) and (3 + 1) and modified f(R) gravity, offering new insights into the initial conditions of the universe First we establish the mathematical and conceptual foundations of the research. We provides an introduction to the canonical quantization of gravity, detailing the Arnowitt-Deser-Misner (ADM) formalism and the construction of the Minisuperspace, which leads to the derivation of the WheelerDeWitt equation. Additionally, we discuss the conceptual challenges associated with quantum cosmology, such as the Problem of Time and examine the boundary condition proposals essential for the tunneling phenomena, alongside an introduction to the fundamental properties of modified f(R) gravity theories. Then we develop the general formalism for calculating vacuum transition probabilities. It introduces a method to compute these probabilities for any Minisuperspace model characterized by a Hamiltonian constraint quadratic in the momenta. A key contribution of this formalism is the systematic incorporation of higher-order terms in the semiclassical expansion, enabling the calculation of quantum corrections to the transition amplitudes".pdfengCIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRAAstronomía--Cosmología--Temas especiales--Cosmología cuánticaFísica--Física atómica--Teorías de la gravitaciónFísica--Física atómica--Física de la relatividad--Tipos especiales de teorías de la relatividadGravedad cuánticaRelatividad general (Física)Tesis de doctoradoopenAccess