Gravidade Modificada e Cosmologia

Abstract

Abstract: Understanding the origin of the current cosmic acceleration is one of the biggest challenges in cosmology nowadays. In the context of the standard cosmological model, this acceleration is assigned to a dark energy through the cosmological constant term $\Lambda$. However, the fact that we do not know the nature of this component, as well as other open issues in the standard model, motivated the interest for alternative scenarios to explain the physics behind the cosmic acceleration. In this sense, it has been proposed several extensions of the General Relativity Theory, such as the introduction of extra fields or extra dimensions or even generalizations of the Ricci scalar, $R$, in the Einstein-Hilbert Lagrangian, by a general function $f(R)$. $f(R)$ theories constitute one of the main extensions of General Relativity, but it is also common to find more general functions involving other scalar quantities like the Gauss-Bonnet invariant curvature, $\mathcal{G}$, built from the Riemann and Ricci tensors. All of these modifications exhibit the common feature of explaining the accelerated expansion without the introduction of an exotic energy component. In this thesis, we analyzed the dynamical and observational viability of $f(R,\mathcal{G})$ gravity theories. First, we perform a dynamical systems analysis for a class of models of type $f(R,\mathcal{G})=\alpha R^{n}\mathcal{G}^{1-n}$ in order to study its cosmological dynamics. From the stability analysis of the fixed points, which are solutions of a system of differential equations representing the dynamical evolution of the Universe, we have shown that this class of theories can not reproduce the sequence of cosmological eras since it does not show a matter dominated epoch. Then, we examined the theoretical predictions of the class of models $f(R,\mathcal{G})=\alpha R^{n}\mathcal{G}^{1-n}$ considering power-law solutions. For that, we compared the theoretical predictions with the recent cosmological observations, including CMB data, SNe Ia data, local measures of the Hubble parameter and large scale structure data. This was done by employing a MCMC analysis in order to constrain the cosmological parameters of the model, which results in new viable accelerated solutions from geometrical terms, that describes well the observational data without consider dark energy. However, the statistical analysis showed strong support in favor of the reference model ($\Lambda$CDM), such that we can discard this model as a cosmologically viable one. Finally, motivated by the recent results showing that the Starobinsky inflationary scenario - $f(R) = R + \alpha R^2$ - is the best fit model to the current CMB data, we explore an extension of this model, based on the equivalence between the $f(R)$ theories and scalar-tensor theories. We discussed the inflationary dynamics of the extended model as well as investigated its theoretical aspects and observational predictions. In this case, the constraints derived are not restrictive because the predictions are very close to that from the $\Lambda$CDM model (inside the $95\%$ confidence region). Therefore, we conclude that it is necessary to perform a complementary analysis considering all the parameter space and using a largest set of observational data.