Perturbações lineares na cosmologia relativística: fundamentos e aplicações

Abstract

This work presents the complete development of the formalism of linear cosmological perturbações in General Relativity. Initially, the foundations of General Relativity are reviewed, including the variational formulation of Einstein’s equations. Next, the cosmology of the FLRW model was constructed, with emphasis on Friedmann’s equations. A central part is dedicated to the formalism of perturbations, addressing the decomposition in scalar, vector and tensor modes, the gauge problem in the description of perturbations, and the construction of gauge-invariant variables, particularly the Bardeen variables. We derive the perturbed Einstein equations for each type of mode and discuss their physical interpretation in the context of the formation of cosmic structures. Finally, the role of cosmic inflation as a mechanism generating primordial perturbations from scalar field fluctuations is analyzed.