Screening of cosmological constant in non-local cosmology

We consider a model of non-local gravity with a large bare cosmological constant, $\mathrm{\Lambda }$, and study its cosmological solutions. The model is characterized by a function $f(\psi )=f_0{e}^{\alpha \psi }$ where $\psi ={\mathrm{\square }}^{-1}R$ and $\alpha$ is a real dimensionless parameter. In the absence of matter, we find an expanding universe solution $a\propto t^n$ with $n<1$, that is, a universe with decelarated expansion without any fine-tuning of the parameter. Thus the effect of the cosmological constant is effectively shielded in this solution. It has been known that solutions in non-local gravity often suffer from the existence of ghost modes. In the present case we find the solution is ghost-free if $\alpha >{\alpha }_{cr}\approx 0.17$. This is quite a weak condition. We argue that the solution is stable against the includion of matter fields. Thus our solution opens up new possibilities for solution to the cosmological constant problem.