Growth of cosmological perturbations in Dark Energy universes

Abstract

In this thesis I focused my attention on dark energy, the mysterious responsible of the observed accelerated expansion rate of our universe. Since the various different models of dark energy are degenerated respect to the observable related only to the expansion history of the universe, I have studied their predictions on the growth of linear perturbations, which provides an additional observable useful to remove the existent degeneracy. However, I found that the actual data related to the growth factor, such as the matter power spectrum from Lyman alpha forests and from 2dF galaxies, the redshift distortion and the baryonic acoustic oscillations cannot put tight constraints on the models, since the errors are still too large. The main models studied in this work are the "coupling model", where dark energy is represented by a scalar field coupled to matter, f(R) models and Dvali-Gabadadze-Porrati model, a class of theories which try to explain the accelerated expansion through modification of standard Einstein gravity. They all give very different predictions for the growth of perturbations with respect to the standard LambaCDM model thus providing a way to discriminate them. Since many experiments in the near future will test dark energy, with unprecedented precision, through its effects on the linear growth of matter perturbations, it is therefore important to find simple yet general parametrizations of the linear growth rate. I showed that a simple fitting formula that generalizes previous expressions reproduces the growth function in models that allow for a growth faster than standard, as for instance in the interacting or scalar-tensor models. This kind of parametrizations turns out to be a very useful tool when one tries to compare the model to observational data. Then I also have parametrized the growth in a large class of models, such as the f(R). The thesis also includes forecasts on the constraints that future data, coming both from satellite or ground based surveys, will put on cosmological parameters such as the growth rate. I used a Fisher matrix approach, using as observable data the information contained in the matter power spectrum, included the one coming from baryonic acoustic oscillations. I found that the improvement in constraining the parameters should be as great as to distinguish among different models.