Cosmological Solutions of a Nonlocal Model with a Perfect Fluid

TL;DR

This paper explores nonlocal gravity models with a specific function form, analyzing power-law solutions in different frames and clarifying their relationships to advance understanding of such models.

Contribution

It provides a comprehensive analysis of power-law solutions in both Jordan and Einstein frames for a nonlocal gravity model with a specific exponential function.

Findings

All available power-law solutions in the Jordan frame are obtained.

New power-law solutions in the Einstein frame are identified.

The relationship between solutions in both frames is clarified and proven to be useful.

Abstract

A nonlocal gravity model which does not assume the existence of a new dimensional parameter in the action and includes a function $f(\Box^{-1} R)$, with $\Box$ the d'Alembertian operator, is studied. By specifying an exponential form for the function f and including a matter sector with a constant equation of state parameter, all available power-law solutions in the Jordan frame are obtained. New power-law solutions in the Einstein frame are also probed. Furthermore, the relationship between power-law solutions in both frames, established through conformal transformation, is substantially clarified. The correspondence between power-law solutions in these two frames is proven to be a very useful tool in order to obtain new solutions in the Einstein frame.