Aspectos de cosmologia e gravitação não local

Abstract

The General Theory of Relativity has been confirmed experimentally by several results since its proposal in 1915. However, it is known that this theory has its validity limit, not being applied to very small length scales and initial times of the universe and does not provide an explanation for the accelerated expansion of the universe. There is still no satisfactory interpretation for the origin of the cosmological constant in the field equations, which describes this expansion in the LCDM cosmological model. Although this model is the most accepted today, it is necessary to postulate the existence of dark energy so that the experimental results are in accordance with the predicted by General Relativity. Due to these and other open questions, several theories have been proposed to minimally modify Einstein’s gravitational theory, such as f (R) theories, non metricity theories and nonlocal theories. In this work we will present the fundamental physical and mathematical concepts of gravitation and cosmology, based on General Relativity. We will present the concept of non-locality in physical theories, through examples of quantum mechanics, electrodynamics and a discussion of non-local gravitation. We will also present a discussion about non-local operators and whether the principle of causality is violated by the presence of non-local terms in an effective quantum action. We will discuss the modified gravity model of Deser-Woodard, which minimally modifies the Einstein-Hilbert action, through nonlocal terms inspired by quantum corrections of effective action. This model was proposed in 2019 in order to explain the accelerated expansion of the universe, without cosmological constant. We will analyze the perturbative solutions of this model, which allow a comparison between theoretical and experimental data for the effective Newtons’s gravitational constant and the growth rate of structures fs8. We will apply the Deser-Woodard model to bouncing universe, finding exact and numerical solutions for the auxiliary fields, which contain non-local information. The results of this analysis show a feasibility of a connection between the bouncing universe and the LCDM model, based on non-local cosmology.