SANTOS, R. S.; SANTOS, Romário da Silva.
Résumé:
The universe is currently in a phase of accelerated expansion, a fact that was proven
experimentally in the late 90’s by two independent research groups. The cosmological
models involving scalar fields allow the description of this regime of accelerated expansion
in the cosmos and present themselves as a promising alternative in the study of the era of
inflation, the primordial period of expansion of the universe. The mechanism responsible
for this phenomenon was called dark energy, which has already received several theoretical
proposals to be described, among which we can highlight the cosmological models of the
quintessence type, where an action composed by a scalar field is coupled to the action of
Einstein -Hilbert. Such a coupling has repercussions on the relative motion equation of
the Lagrangian density of the scalar field, as well as on the Friedmann equations, derived
from the minimization of the action with respect to the metric. This procedure clearly
shows that this scalar field will influence the determination of the cosmological parameters.
In this dissertation we hope to understand the process of expansion of the accelerated
universe using the solutions of the Friedmann equations and some relevant cosmological
parameters, and for this, we will present a methodology capable of constructing new families
of potentials composed by a scalar field and two functions of modified gravity, being one
of type f(R, T) and a function Λ(φ) that varies over time. Thus, we will construct
an analytical model of links between these models and will study if the cosmological
parameters derived from this proposal are consistent from two examples of known models,
verifying if the results corroborate with the description of different phases of the universe.
