On the Graviton Mass

It was suggested that observations of the solar system exclude massive gravity, in the sense that the graviton mass must be rigorously zero. This is because there is a discontinuity in the linearized gravity theory at graviton mass equal to zero. The linearized Schwarzschild metric is not recovered for infinitesimal graviton mass, contradicting observations on light deviation by the Sun and Mercury perihelion advance. It was then argued that non-perturbative effects make the massive gravity theory continuous in the graviton mass. Both the original suggestion and its refutation were based on a non-covariant and linearized action, and the physical interpretation of these results remained questionable. Here we use a covariant quasi-massive gravity theory that is known to be discontinuous in the graviton mass in the linear approximation. We show that non-perturbative effects do restore the continuity; the weak-field Schwarzschild solution is recovered in the limit of small graviton mass. We also show that weak-field Schwarzschild with matter is recovered for infinitesimal graviton mass. Thus: Observations of the solar system only put an upper limit on the graviton mass (in the context of the gravity theory that we use, inverse graviton mass, as measured at distances of order inverse graviton mass, is $\gtrsim 100$ Mpc). But graviton can be massive, with a cosmologically interesting mass.