Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity

TL;DR

This paper explores non-local gravity modifications involving inverse d'Alembertian of Ricci scalar, demonstrating stable dark energy solutions with varying equations of state, including phantom and non-phantom phases, without negative kinetic energy fields.

Contribution

It introduces a specific non-local gravity model with exponential dependence on inverse d'Alembertian, analyzing its cosmological dynamics and stability of dark energy solutions.

Findings

Existence of stable dark energy fixed points with varying equations of state.

Phantom and non-phantom behaviors depend on parameter lpha.

Late-time universe can mimic dust and accelerate without negative kinetic energy.

Abstract

In this paper we have investigated the cosmological dynamics of non-locally corrected gravity involving a function of the inverse d'Alembertian of the Ricci scalar, $f(\Box^{-1} R))$. Casting the dynamical equations into local form, we derive the fixed points of the dynamics and demonstrate the existence and stability of a one parameter family of dark energy solutions for a simple choice, $f(\Box^{-1} R)\sim \exp(\alpha \Box^{-1} R)$. The effective EoS parameter is given by, $w_{\rm eff}=({\alpha-1})/({3\alpha-1})$ and the stability of the solutions is guaranteed provided that $1/3<\alpha<2/3$. For $1/3<\alpha<1/2$ and $1/2<\alpha<2/3$, the underlying system exhibits phantom and non-phantom behavior respectively; the de Sitter solution corresponds to $\alpha=1/2$. For a wide range of initial conditions, the system mimics dust like behavior before reaching the stable fixed point. The late time phantom phase is achieved without involving negative kinetic energy fields. A brief discussion on the entropy of de Sitter space in non-local model is included.