Some cosmological and astrophysical aspects of modified gravity theories

This thesis will try to contribute to the understanding of open issues in cosmology by considering f® and brane-world theories. In Chapter 1, we shall summarize the main features of f® gravities in the metric formalism and we shall introduce both the notion of brane excitations, the branons, and the brane-skyrmions. We shall finish the chapter by providing some insight about the possibility of mini black holes detection in the LHC as a signature for the validity of these modified gravity theories. The Chapter 2 will deal with f® theories able to mimic Einstein-Hilbert plus cosmological constant solutions and f® theories will be shown to be able to mimic the cosmological evolution generated by any perfect fluid with constant equation of state. The Chapter 3 will be devoted to the computation of cosmological perturbations for f® theories. Special attention will be paid here to obtain a completely general differential equation for the evolution of perturbations and its particularization for the so-called sub-Hubble scales will be explicitly shown. In the Chapter 4 we shall focus on the study of black holes in f® gravities in an arbitrary number of dimensions. With this purpose we shall study constant curvature solutions for f® theories as well as perturbative solutions around the standard SAdS geometry. An important part of this chapter will be then devoted to the thermodynamics of SAdS black holes in f® theories. In the Chapter 5 we will thoroughly study brane-skyrmions. In this context, the recent claim of detection of an unexpected feature in the CMB, referred to as the cold spot, will be explained as a topological defect on the brane in complete agreement with those calculations in the literature that tried to explain that cold spot as a texture of a NLSM. Main conclusions are summarized all together in Chapter 6 .