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

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, $f({\square }^{-1}R))$. 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, $f({\square }^{-1}R)\sim \exp (\alpha {\square }^{-1}R)$. The effective EoS parameter is given by, $w_{\mathrm{eff}}=(\alpha -1)/(3\alpha -1)$ 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.

arXiv comment5 pages and 2 figures, typos corrected, final version to appear in Phys. Lett. B

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