Stability analysis and future singularity of the $m^2 R \Box^{-2} R$ model of non-local gravity

Recently, Maggiore and Mancarella proposed a non-local modification of General Relativity to account for the effect of dark energy. In this paper we contribute to the study of this model by analysing its stability on the relevant space-times for solar system and cosmological physics. We show that these solutions are stable under small perturbations because the latter are "diluted" by the violent expansion of the cosmological background at late times. Indeed, the universe expands so rapidly that any finite volume becomes eventually infinite at a finite time, a scenario which goes by the name "big rip".