Abstract:
In the present work, we review some general aspects of modified gravity theories,
investigating mathematical and physical properties and, more specifically, the
feature of viable and realistic models able to reproduce the dark energy epoch and
the early-time inflation. We will discuss the black hole solutions in generalized
theories of gravity: it is of fundamental interest to understand how properties and
laws of black holes in General Relativity can be addressed in the framework of
modified theories. In particular, we will discuss the energy issue and the possibility
to derive the First Law of thermodynamics from the field equations. Then, in the
analysis of cosmological solutions, we will pay a particular attention to the
occurrence of finite-time future singularities and to the possibility to avoid them
in F(R,G)-gravity. Furthermore, realistic models of F(R)-gravity will be analyzed
in the detail. A general feature occurring in matter era will be shown, namely the
high derivatives of Hubble parameter may be influenced by the high frequency
oscillation of the dark energy and some correction term is required in order to
stabilize the theory at high redshift. The inflationary scenario is also carefully
analyzed and an unified description of the universe is risen. In the final part of the
work, we will have a look at the last developments in modified gravity, namely we
will investigate cosmological and black hole solutions in a covariant field theory of
gravity and we will introduce the extended “teleparallel” F(T)-gravity theories. A
nice application to the dark matter problem will be presented.
