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(R) and brane-world theories. In Chapter 1, we shall
summarize the main features of f(R) 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(R) theories able to mimic Einstein-Hilbert
plus cosmological constant solutions and f(R) 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(R) 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(R) gravities
in an arbitrary number of dimensions. With this purpose we shall study constant
curvature solutions for f(R) 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(R) 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 .
