A New Model of Nonlocal Modified Gravity

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

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