Non-local massive gravity and dark energy
We propose an infrared modification of General Relativity, based on the addition of non-local terms to the Einstein equations. This construction provides a theory of massive gravity which is fully covariant, without the need of introducing an external reference metric. We discuss the consistency of the theory and its cosmological consequences. We find that the model generates a dynamical dark energy that can account for the presently observed value, without introducing a cosmological constant. Tuning a free mass parameter to a value $m= 0.67 H_0$ we reproduce the observed value $\Omega_{DE}\simeq 0.68$. 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 $w_0= -1.040$ and $w_a= -0.020$, consistent with the Planck data, and on the phantom side. We also show that the model displays a sort of degravitation mechanism where the cosmological constant is reabsorbed into the boundary conditions of a scalar field.