Reconstrução Não Paramétrica das Perturbações Cosmológicas

Abstract

The current large astronomical surveys have allowed us access to a growing quantity and quality of observational data. For this reason, it is necessary to explore different techniques to model and extract the maximum information from these data. The main approach used to model the observations is the parametric one where it is proposed a functional form to describe the behaviour of the data, leaving in the statistical analysis the restriction of the free parameters of our initial model. In recent years, non-parametric methods have been used more frequently, where an a priori functional behaviour of the data is not assumed, obtaining results less biased by the arbitrary choice of the experimenter. In this case, the results are model independent. In this thesis, we have studied some of the most successful non-parametric methods in the area of cosmology and applied them to specific problems of great interest in the study of the cosmic acceleration. Thus, our main objective is to obtain cosmological-model-independent results from the most recent astronomical surveys data. % First, we apply the non-parametric methods, so-called Gaussian Processes and Non-Parametric Smoothing, to reconstruct the Hubble parameter from galaxy ages observations in low and intermediate redshifts. These data are considered to be cosmological and stellar population model independent. For this reason, it is expected that our results are bias free because both the statistical methods and data are model independent. This expansion rate reconstruction is used to calibrate SNe Ia and study their implications on the standard cosmological model. In the second part, in order to break the existing degeneracy at the background level between dark energy models and modified gravity theories, we explore the cosmological matter perturbations at the linear regime characterized by the matter density contrast, the growth rate and the growth index. We apply non-parametric methods to galaxy ages and high-$z$ quasars $ H(z) $ data. With the expansion rate information, the current matter density parameter -given by Planck and WMAP collaborations- and assuming that the Universe is homogeneous and isotropic and General Relativity as a theory of gravitation, we reconstruct the matter perturbations and compare them with the estimates of the matter perturbation quantities from the mapping of the large-scale structure of the Universe. In addition, we calculated a null test of the standard cosmological model using background and perturbative quantities. We find a tension ($\sim 3 \sigma$) depending on the current matter density parameter assumed in the calculation. Finally, we generalize the solution of the perturbative quantities to modified gravity scenarios. In this case, we find a good agreement with our calculations from the non-parametric reconstruction of the cosmic expansion and the theoretical ones. We conclude that reconstructions of matter perturbations from background observables may be an effective method to distinguish modified gravity theories, mainly with the advent of high quality data from the mapping of the large-scale structure of the Universe.