Starobinsky Inflation And The Order Reduction Technique
Name: WALESKA PRISCYLLA FLORENCIO DE MEDEIROS
Type: PhD thesis
Publication date: 03/10/2022
Advisor:
Name |
Role |
|---|---|
| OLIVER FABIO PIATTELLA | Advisor * |
Examining board:
| Name |
Role |
|---|---|
| ILIA CHAPIRO | Internal Examiner * |
| JÚLIO CÉSAR FABRIS | Co advisor * |
| OLIVER FABIO PIATTELLA | Advisor * |
Summary: The order reduction technique (ORT) is an iterative method of solution of higher order differential 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 differential equations. Fortunately, as it is known in the literature, the order reduction method presents fewer solutions, and with that, one of the intentions of the technique is to make it easier to select the solutions which present a 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 inflationary 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.
