Some Cosmological Solutions of a Nonlocal Modified Gravity

TL;DR

This paper explores nonlocal modifications to Einstein's gravity, deriving equations of motion and finding cosmological solutions with constant Ricci scalar within a pseudo-Riemannian framework.

Contribution

It introduces a new class of nonlocal gravity models with a specific form of nonlocal term and derives their equations of motion, providing cosmological solutions.

Findings

Derived equations of motion for nonlocal gravity models.

Found cosmological solutions with constant Ricci scalar.

Extended the framework of modified gravity theories.

Abstract

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.