Starobinsky Inflation And The Order Reduction Technique

• Ano de defesa: 2022
• Autor(a) principal: Medeiros, Waleska Priscylla Florencio de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Espírito Santo; BR; Doutorado em Astrofísica, Cosmologia e Gravitação; Centro de Ciências Exatas; UFES; Programa de Pós-Graduação em Astrofísica, Cosmologia e Gravitação
• Palavras-chave em Português: Técnica de redução de ordem; Oscilador harmônico; Inflação de Starobinsky; subject.br-rjbn; Astronomia
• Link de acesso: http://repositorio.ufes.br/handle/10/16287

The order reduction technique (ORT) is an iterative method of solution of higher order di erential equations. It consists of treating the higher order terms perturbatively so that the lower order in the order reduction must be chosen according to which regime of solution the method is going to reproduce. In some cases, the presence of solutions that do not have physical behavior is observed, mainly associated with particularly higher order di erential equations. Nonetheless, as it is known in the literature, the order reduction method presents a smaller number of solutions, and with that, one of the intentions of the technique is to make it easier to select the solutions that present good physical behavior. However, it must be emphasized that one disadvantage of the method is that there could be some physical solutions that the order reduction will not detect. The ORT is applied to the following cases: 1. The study of the dynamics of the motion of a charged particle. 2. The harmonic oscillator. 3. The in ationary paradigm of Starobinsky. We show that, in the case of the examples cited above, the ORT as an iterative perturbative method does not show convergence in the oscillating regime of a weak coupling limit. This regime is excluded by the order reduction. In addition, the method shows good convergence in the strong coupling regime, non-oscillating which slowly approaches equilibrium. The main results discussed are based on the work [1].