New Cosmological Solutions of a Nonlocal Gravity Model

TL;DR

This paper explores new exact cosmological solutions in a nonlocal gravity model, including nonflat space solutions and potential topology changes, extending previous flat space solutions and examining model symmetries.

Contribution

It introduces additional exact solutions in nonflat space for a nonlocal gravity model and discusses model extensions with symmetric nonlocal operators.

Findings

Discovered new cosmological solutions in nonflat space.

Showed nonlocal dynamics can alter background topology.

Connected the model to other nonlocal gravity frameworks.

Abstract

A nonlocal gravity model (2.1) was introduced and considered recently [49], and two exact cosmological solutions in flat space were presented. The first solution is related to some radiation effects generated by nonlocal dynamics on dark energy background, while the second one is a nonsingular time symmetric bounce. In the present paper we investigate other possible exact cosmological solutions and find some the new ones in nonflat space. Used nonlocal gravity dynamics can change background topology. To solve the corresponding eqations of motion, we first look for a solution of the eigenvalue problem $\Box (R -4\Lambda) = q\ (R - 4\Lambda) .$ We also discuss possible extension of this model with nonlocal operator symmetric under $\Box \longleftrightarrow \Box^{-1}$ and its connection with another interesting nonlocal gravity model.