De Sitter Universe in Nonlocal Gravity

TL;DR

This paper investigates de Sitter solutions in a nonlocal gravity model involving a function of the inverse d'Alembertian of Ricci scalar, analyzing their stability and deriving new solutions with dark matter considerations.

Contribution

It demonstrates conditions for de Sitter solutions in nonlocal gravity and explores their stability, including new solutions with dark matter effects.

Findings

De Sitter solutions exist only if the function f satisfies a specific differential equation.

Stable de Sitter solutions are found for positive Hubble parameter values.

New solutions incorporating dark matter are derived and shown to be stable.

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 considered. The model is proven to have de Sitter solutions only if the function f satisfies a certain second-order linear differential equation. The de Sitter solutions corresponding to the simplest case, an exponential function f, are explored, without any restrictions on the parameters. If the value of the Hubble parameter is positive, the de Sitter solution is stable at late times, both for negative and for positive values of the cosmological constant. Also, the stability of the solutions with zero cosmological constant is discussed and sufficient conditions for it are established in this case. New de Sitter solutions are obtained which correspond to the model with dark matter and stability is proven in this situation for nonzero values of the cosmological constant.