Thesis defense
Student: Pedro Eleutério Mendonça de Almeida
Program: Astronomy
Title: "Decaying Vacuum Cosmologies and its Non-Canonical Scalar Field Description"
Advisor: Prof. Dr. José Ademir Sales de Lima
Judging Committee
Presidente da banca: Prof. Dr. José Ademir Sales de Lima (orientador) - IAG-USP
- Prof. Dr. Laerte Sodré Júnior - IAG/USP
- Prof. Dr. Airton Deppman - IF/USP
- Prof. Dr. Nelson de Oliveira Yokomizo – UFMG (por videoconferência)
- Prof. Dr. Valdir Barbosa Bezerra – UFPB (por videoconferência)
- Prof. Dr. José Fernando de Jesus – UNESP (por videoconferência)
Abstract
Motivated by the observational and theoretical challenges faced by the standard cosmological model ($\Lambda$CDM), we investigate the viability of a class of models with $\Lambda(H)$, or vacuum decay. We discuss the dynamics and thermodynamics of these models, presenting their main virtues and proposals for solving the issues of the $\Lambda$CDM model. We show that in these models, the Universe begins from an initial de Sitter stage where the accelerated expansion of the Universe is governed by a very high energy scale $\lesssim M_P$. Subsequently, the model follows the traditional evolution, transitioning through radiation-, matter-, and dark energy-dominated eras, culminating in a final de Sitter stage. This class of models avoids the initial singularity, provides a solution to the horizon problem, unifies the mechanisms of the Universe's acceleration, and proposes an inflationary scenario that emerges naturally. We present a thermodynamic approach in which we derive the relationship between the particle production rate and vacuum decay, assuming that the specific entropy of the produced particles remains constant. We also demonstrate how to obtain a description using non-canonical scalar fields for this class of models. In this description, all the field's energy is initially stored in the potential, which describes the vacuum energy density. Over time, the potential transfers energy to the kinetic term (radiation energy density), whose equation of state is $p = \rho/3$. By the end of the vacuum decay process, the remaining energy is entirely stored in radiation, with no supercooling or reheating required. Finally, we present the conditions under which the slow-roll approximation is valid in this description and determine the initial power spectrum under these conditions. This result enables the study of large-scale structure formation within this model.
Keywords: Cosmology, Inflation, Dark Energy, Vacuum Decay, de Sitter Stage, Non-Canonical Scalar Fields.