Gravitational models with non-local scalar fields

TL;DR

This paper explores a broad class of f(R) gravity models incorporating nonlocal scalar fields, proposing methods for localization and analyzing solutions with complex roots in the operator F(□).

Contribution

It introduces a localization approach for nonlocal gravitational models with quadratic potentials and arbitrary analytic functions, enabling the derivation of particular solutions.

Findings

Localization method for nonlocal models developed

Solutions found for models with simple and double roots in F(□)

Framework applicable to a wide class of nonlocal gravity theories

Abstract

A general class of f(R) gravity models with minimally coupling a nonlocal scalar field is considered. The Ostrogradski representation for nonlocal gravitational models with a quadratic potential and the way of its localization are proposed. We study the action with an arbitrary analytic function $F(\Box)$, which has both simple and double roots. The way of localization allows to find particular solutions of nonlocal equations of gravity.