Non-local massive gravity

We present a general covariant action for massive gravity merging together a class of “non-polynomial” and super-renormalizable or finite theories of gravity with the non-local theory of gravity recently proposed by Jaccard, Maggiore and Mitsou (Phys. Rev. D 88 (2013) 044033). Our diffeomorphism invariant action gives rise to the equations of motion appearing in non-local massive gravity plus quadratic curvature terms. Not only the massive graviton propagator reduces smoothly to the massless one without a vDVZ discontinuity, but also our finite theory of gravity is unitary at tree level around the Minkowski background. We also show that, as long as the graviton mass m is much smaller the todayʼs Hubble parameter H0, a late-time cosmic acceleration can be realized without a dark energy component due to the growth of a scalar degree of freedom. In the presence of the cosmological constant Λ, the dominance of the non-local mass term leads to a kind of “degravitation” for Λ at the late cosmological epoch.