New Cosmological Solutions of a Nonlocal Gravity Model

Ivan Dimitrijevic,Jelena Stankovic,Branko Dragovich,Zoran Rakic

doi:10.3390/sym14010003

Abstract

A nonlocal gravity model (2) was introduced and considered recently, 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 the background topology. To solve the corresponding equations of motion, we first look for a solution of the eigenvalue problem □(R−4Λ)=q(R−4Λ). We also discuss possible extension of this model with a nonlocal operator, symmetric under □⟷□−1, and its connection with another interesting nonlocal gravity model.

Highlights

The current standard model of cosmology (SMC) [1], known as the ΛCDM model, assumes general relativity (GR) [2] as the theory of the gravitational interaction at all cosmic space-time scales—galactic and cosmological
By the ΛCDM model, dark matter is responsible for observational dynamics inside and between galaxies, while dark energy causes accelerated expansion of the universe
The ΛCDM model asserts that dark energy (DE) corresponds to the cosmological constant and that DM is in a cold state

Summary

Introduction

The current standard model of cosmology (SMC) [1], known as the ΛCDM model, assumes general relativity (GR) [2] as the theory of the gravitational interaction at all cosmic space-time scales—galactic and cosmological. It includes nonlocal extension of the Starobinsky R2 inflation model [28,29] This kind of nonlocal investigation started in [16,17] and is an attempt to find a nonsingular bouncing solution of the singularity problem in s√tandard cosmology. The first term R − 2Λ = R − 2Λ R − 2Λ remains unchanged in the linear approximation As it is already mentioned in Introduction, the nonlocal gravity model (3) is very interesting and promising. The step in the investigation of nonlocal gravity model (2) is finding the corresponding equations of motion (EOM). It is done for a class of models (1) that contain (2); the derivation is presented in [39]. In finding the cosmological solutions, we start from Equation (21)

Cosmological Solutions

Two Previous Exact Solutions

Findings

Discussion and Conclusions

Conclusions