Screening of cosmological constant in non-local gravity

We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of of non-local gravity with the Lagrangian of the form, $R+f({\mathrm{\square }}^{-1}R)-2\mathrm{\Lambda }$ where $f(X)$ is a quadratic function of $X$, there is a flat spacetime solution despite the presence of the cosmological constant $\mathrm{\Lambda }$. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of `time’. Nevertheless our result suggests the possibility of solving the cosmological constant problem in the context of non-local gravity.