Screening of cosmological constant for De Sitter Universe in non-local
  gravity, phantom-divide crossing and finite-time future singularities
  We investigate de Sitter solutions in non-local gravity as well as in
non-local gravity with Lagrange constraint multiplier. We examine a condition
to avoid a ghost and discuss a screening scenario for a cosmological constant
in de Sitter solutions. Furthermore, we explicitly demonstrate that three types
of the finite-time future singularities can occur in non-local gravity and
explore their properties. In addition, we evaluate the effective equation of
state for the universe and show that the late-time accelerating universe may be
effectively the quintessence, cosmological constant or phantom-like phases. In
particular, it is found that there is a case in which a crossing of the phantom
divide from the non-phantom (quintessence) phase to the phantom one can be
realized when a finite-time future singularity occurs. Moreover, it is
demonstrated that the addition of an $R^2$ term can cure the finite-time future
singularities in non-local gravity. It is also suggested that in the framework
of non-local gravity, adding an $R^2$ term leads to possible unification of the
early-time inflation with the late-time cosmic acceleration.
