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We investigate de Sitter solutions in non-local gravity as well as innon-local gravity with Lagrange constraint multiplier. We examine a conditionto avoid a ghost and discuss a screening scenario for a cosmological constantin de Sitter solutions. Furthermore, we explicitly demonstrate that three typesof the finite-time future singularities can occur in non-local gravity andexplore their properties. In addition, we evaluate the effective equation ofstate for the universe and show that the late-time accelerating universe may beeffectively the quintessence, cosmological constant or phantom-like phases. Inparticular, it is found that there is a case in which a crossing of the phantomdivide from the non-phantom (quintessence) phase to the phantom one can berealized when a finite-time future singularity occurs. Moreover, it isdemonstrated that the addition of an $R^2$ term can cure the finite-time futuresingularities in non-local gravity. It is also suggested that in the frameworkof non-local gravity, adding an $R^2$ term leads to possible unification of theearly-time inflation with the late-time cosmic acceleration.

Screening of cosmological constant for De Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities