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 non-local gravity with the Lagrangian of the form, R + f (rectangle(-1) R) - 2 Lambda where f (X) is a quadratic function of X, there is a flat spacetime solution despite the presence of the cosmological constant 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. (C) 2010 Elsevier B.V. All rights reserved.