Cosmology and dynamical systems: the relationship between the scale factor and cosmological fields.

In order to put a spotlight on the fundamental fields that shape the cosmic dynamics, this thesis discusses in an introductive manner the connection between the realms of dynamical systems theory and Cosmology. The primary objective is to discuss how mathematical models can be employed to comprehend the complex dynamics governing the observable universe, by yielding a nonlinear coupling between the scale factor, on one hand, and a possible cosmological field, permeating the space at cosmological scale, on the other. This thesis begins introducting the Lagrangian formalism applicable to cosmological fields, processing towards an exploration of the Einstein Field Equations and Friedmann solutions, and finally, delving into the dynamics of scalar-tensor theories and how they affect the scale factor’s evolution. A fundamental reference for this exploration, especially in the final chapter, is the ELSEVIER-published article titled ’Dynamical Systems Applied to Cosmology: dark energy and modified gravity’ (2018). This article serves as a keystone, guiding the main considerations on cosmological models influenced by dark energy.