Phantom dark energy from non-local infrared modifications of General Relativity

Abstract: We discuss the cosmological consequences of a model based on a non-local infrared modification of Einstein equations. We find that the model generates a dynamical dark energy that can account for the presently observed value of $\Omega_{\rm DE}$, without introducing a cosmological constant. Tuning a free mass parameter $m$ to a value $m\simeq 0.67 H_0$ we reproduce the observed value $\Omega_{\rm DE}\simeq 0.68$. This leaves us with no free parameter and we then get a pure prediction for the EOS parameter of dark energy. Writing $w_{\rm DE}(a)=w_0+(1-a) w_a$, we find $w_0\simeq-1.04$ and $w_a\simeq -0.02$, consistent with the Planck data, and on the phantom side. We also argue that non-local equations of the type that we propose must be understood as purely classical effective equations, such as those derived in semiclassical gravity for the in-in matrix elements of the metric. As such, any apparent ghost instability in such equations only affects the classical dynamics, but there is no propagating degree of freedom associated to the ghost, and no issue of ghost-induced quantum vacuum decay.