Some Cosmological Solutions of a Nonlocal Modified Gravity

Understand

We consider nonlocal modification of the Einstein theory of gravity in framework of the pseudo-Riemannian geometry.

• The nonlocal term has the form $\mathcal{H}(R) \mathcal{F}(\Box)\mathcal {G}(R)$, where $\mathcal{H}$ and $\mathcal{G}$ are differentiable functions of the scalar curvature $R,$ and $ \mathcal{F}(\Box)= \displaystyle \sum_{n =0}^{\infty} f_{n}\Box^{n}$ is an analytic function of the d'Alambert operator $\Box .$ Using calculus of variations of the action functional, we derived the corresponding equations of motion.
• The variation of action is induced by variation of the gravitational field, which is the metric tensor $g_{\mu\nu}$.
• Cosmological solutions are found for the case when the Ricci scalar $R$ is constant.