Resumo:
In this thesis, a qualitative analysis is proposed on how theories related to gravity have
changed over time until reaching the well-known modified theories of gravitation, demonstrating
the power they hold. The aim is to serve as an entry point to the subject and
provide a basis for more complex works in the future. Starting with the understanding of
gravity and progressing to Albert Einstein’s groundbreaking theory of General Relativity,
which explained some aspects not addressed by Newtonian theory but still left unexplained
observations on large scales. After Einstein, efforts have been mostly focused on constructing
extensions of General Relativity, paving the way for the well-known modified theories
of gravitation. These theories manifest in various forms in the literature, but here the
focus will be on those constructed by the inclusion of a scalar field into the theory, giving
rise to the so called scalar-tensor theories. Among the modified scalar-tensor theories, the
discussion will be restricted to those that preserve second-order equations of motion, with
the most general known as the Horndeski theory, which will be the main theory addressed
here. After dissecting the Horndeski theory, we analyze its equations of motion and apply
the latter to certain cases of interest. The general aspect of the Horndeski theory will
also be exploited to derive, from it, already known theories, such as Brans-Dicke, Cubic
Galileon, and 𝑓 (𝑅) models. The final part of the work will be dedicated to delving into
quantum cosmology using the Horndeski theory.
