Non-local gravity and dark energy

Abstract: We discuss a nonlocal modification of gravity obtained adding a term $m^2 R\,\Box^{-2}R$ to the Einstein-Hilbert action. We find that the mass parameter $m$ only affects the non-radiative sector of the theory, while the graviton remains massless, there is no propagating ghost-like degree of freedom, no vDVZ discontinuity, and no Vainshtein radius below which the theory becomes strongly coupled. For $m={\cal O}(H_0)$ the theory therefore recovers all successes of GR at solar system and lab scales, and only deviates from it at cosmological scales. We examine the cosmological consequences of the model and we find that it automatically generates a dynamical dark energy and a self-accelerating evolution. After fixing our only free parameter $m$ so to reproduce the observed value of the dark energy density today, we get a pure prediction for the dark energy equation of state, $w_ {\rm DE}\simeq-1.14$. This value is consistent with the existing data, and could also resolve the possible tension between the Planck data and local measurements of the Hubble parameter.