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

In this Letter we have investigated the cosmological dynamics of non-locally corrected gravity involving a function of the inverse d'Alembertian of the Ricci scalar, f(□−1R). 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(□−1R)∼exp(α□−1R). The effective EoS parameter is given by, weff=(α−1)/(3α−1) and the stability of the solutions is guaranteed provided that 1/3<α<2/3. For 1/3<α<1/2 and 1/2<α<2/3, the underlying system exhibits phantom and non-phantom behavior respectively; the de Sitter solution corresponds to α=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.