Localization of the SFT inspired Nonlocal Linear Models and Exact Solutions

TL;DR

This paper explores a broad class of nonlocal gravitational models with scalar fields, providing a method to localize the equations and presenting exact solutions in cosmological metrics.

Contribution

It generalizes localization techniques for nonlocal Einstein equations to models with linear potentials and derives exact solutions in specific cosmological settings.

Findings

Localization method for nonlocal Einstein equations with linear potentials

Exact solutions in Friedmann-Robertson-Walker metric

Exact solutions in Bianchi I metric

Abstract

A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. We study the action with an arbitrary analytic function $F(\Box)$, which has both simple and double roots. The way of localization of nonlocal Einstein equations is generalized on models with linear potentials. Exact solutions in the Friedmann-Robertson-Walker and Bianchi I metrics are presented.