A New Model of Nonlocal Modified Gravity

We consider a new modified gravity model with nonlocal term of the form $R^{-1}\mathcal{F}(\mathrm{\square })R\mathrm{.}$ This kind of nonlocality is motivated by investigation of applicability of a few unusual ans"atze to obtain some exact cosmological solutions. In particular, we find attractive and useful quadratic ansatz $\mathrm{\square }R=q{R}^2\mathrm{.}$