Accelerated expansion as manifestation of gravity: when Dark Energy
  belongs to the left
  In order to explain the Late-times accelerated expansion of the Universe we
must appeal to some form of Dark Energy. In the standard model of cosmology,
the latter is interpreted as a Cosmological Constant $\Lambda$. However, for a
number of reasons, a Cosmological Constant is not completely satisfactory. In
this thesis we study Dark Energy models of geometrical nature, and thus a
manifestation of the underlying gravitational theory. In the first part of the
thesis we will review the $\Lambda$CDM model and give a brief classification of
the landscape of alternative Dark Energy candidates based on the Lovelock
theorem. The second part of the thesis is instead devoted to the presentation
of our main results on the topic of Dark Energy. To begin with, we will report
our studies about nonlocal modifications of gravity involving the differential
operator $\Box^{-1}R$, with emphasis on a specific model and on the common
behavior shared by this and similar theories in the late stages of the
evolution of the Universe. Then we introduce a novel class of modified gravity
theories based on the anticurvature tensor $A^{\mu\nu}$ (the inverse of the
Ricci tensor), and assess their capability as source of Dark Energy. Finally,
we will discuss a type of drift effects which we predicted in the contest of
Strong Gravitational Lensing, which could be employed both to study the
effective equation of state of the Universe and to constrain violations of the
Equivalence Principle.
